This is a good question for the "un-initiated". Just buy a game card and start playing. Cataclysm is coming but it's a few gigabytes of updates. Blizzard's launcher is pretty smart by pre-downloading content ahead of release, so you can just log on and play when it's officially released. So, to avoid disappointment with Cataclysm. Start downloading now.
PVP or PVE?
With PVP realms, there is a thing called "ganking", (Arqade discussion on ganking here), where groups of players just wait in ambush and just smack you senseless whilst travelling between cities or trying to complete quests for no reason apart from bulling players. If you like that sort of stuff, and want to PVP you can go this route. It does waste a lot of time when you want to go questing/farming and generally getting gear, though.
PVE has battlegrounds where you can engage in PVP play. I prefer PVE because you can get into PVP at your choosing, rather than getting ambushed every 10 minutes. PVE it's just you vs the environment. Not other players. PVE also has duelling. So, you can also pick a fight when you want to.
As a casual gamer. There is a built in quest helper, so this can speed up the grind of going around completing quests. If you're not playing constantly, then there is value in logging off in taverns and major cities, because you gain "rested XP" faster in taverns and cities, rather than logging off in the forests/roads. Rested XP basically is worth double the normal XP from kills and quests. You will level faster that way.
Best guides I have found are these:
Addons
Add-ons are enhancements to your WoW interface that can really improve game play. They have become an industry in itself, although Blizzard discourages people paying for them, you can get them for free.
You can find wow addons on Curse.
I use Auctioneer among others, but a good list of what's popular can be found here. There are class specific addons as well and you can keep them up to date with wowmatrix.
Instances
If you like raiding, I recommend that you get good at the 5 man dungeons (also known as "instances"). The key thing about instances or raids is to know the role you play in the group. It boils down to 3 different types, Damage dealers/Tanks/Healers. They're self explanatory, but Tanks are basically the one player who tries to hold the attention of the big boss you will end up fighting. This is so the damage dealers can kill it, and the healers, well... heal everyone.
Holding their attention, is called "holding threat". As the bosses or any mob you are fighting does a calculation to determine who they should kill, by estimating who presents the biggest threat. So, damage dealers tend to have high threat, because of their DPS (Damage Per Second). Healers can gain threat, because they're keeping everyone very healthy. You can improve your level of threat through talents or buffs. (A buff is like drinking a potion or a beneficial spell that gives you a special attribute for a period of time). You'll learn about which buffs are important to your style of gameplay as you progress. Finally, each instance tends to have anywhere from 3-12 bosses. You don't have to wait til you're level 80 to do raids, you can do them through level ranges of character, but the first one to do would be Stockades in Stormwind (if you're alliance), when you're about level 15, and you should go in with at least one or 2 other players of similar level. You can find dungeon groups through the dungeon finder. There is also a "raid browser". It's all built into WoW. The trade chat channel tends to have lots of offers/requests for player to join raid groups. If you do get hooked on raiding (as I expect you will), better to look for a guild to join because once you start doing 10man or 25 man raids, you need a reliable group of people to run the instances, because random or ad hoc groups can be painful, if you get the wrong group of people together.
Terminology in WoW
Basic dialog/lingo in the trade channel is like this.
LFM = Looking For More.
LFG = Looking For Group.
GS= gearscore
So, someone might say LFM Ony= Looking For More players to do the Onyxia instance. or Say LFM ICC min gs5500 = "Looking for more for Ice Crown citadel, minimum gearscore is 5500". You'll get to know the lingo as chat with people.
Trade chat is global across all cities. But only available in the cities. You can't see trade chat outside of cities.
Also, you might hear about "Gearscore". This relates to the quality of all your gear you wear. Each item you have has an "item level". The higher the item level, the better suited you are for the harder instances. The top item level (pre-cataclysm) is 264.
Gear and Items
You can acquire great gear by making it/buying it/looting it. The auction house can be good in this way to buy gear from other players. You can also buy very exotic gear from special merchants using tokens. There is a large array of currencies for different levels of gear. Blizzard are now unifying it, you got 2 basic "token" currencies, Justice Points and Honor points, (This is different from gold/silver/bronze). You earn them by doing raids or PVP. There is also some gear that you can buy from merchants, by trading other exotic items, but this is the highest level stuff (level 80).
The quality of gear you have determines whether you can do higher level instances. That's what Gearscore works out for you. There is an addon for gearscore. Get it. Players will sometime ask for people who only have a certain level of gear. They're basically trying to keep out the riff-raff, so these can be good raids to get into even though they are ad-hoc. This is common for trying to do ICC (Ice Crown Citadel instance).
At the end of the day, just do whatever you find fun in.
MMO-Champion has posted this excellent map of the zone flow from 1-85 post-shattering:
A more detailed breakdown can be found at WoWPedia
In short, Eastern Kingdoms goes Tirsifal → Silverpine → Hillsbrad → Arathi → Hinterlands → Western Plaguelands → Eastern Plaguelands → Badlands → Searing Gorge → Burning Steppes → Blasted Lands.
Kalimdor goes Mulgore/Durotar → Northern Barrens/Azshara → Ashenvale → Stonetalon Mountains → Desolace → Feralas → Thousand Needles → Tanaris → Un'Goro → Silithus.
Alternately, you can jump off the path after Hillsbrad/Ashenvale, head to Northern Stranglethorn, and continue from there into Southern Stranglethorn, South Barrens, Dustwallow Marsh, before rejoining the Kalimdor path at Thousand Needles.
After completing Thousand Needles or Western Plaguelands, you again have the opportunity to jump paths, and can follow quests through Felwood and Winterspring instead, though you may need to hop back to Silithius and/or Blasted Lands to get the last few levels you need before Outland if you go that route.
Best Answer
Okay, I spent some time checking Wowhead and thinking back to my experiences, and I think I have a non-PvP, mostly non-"dungeon grind" progression path you can use.
I've also added a citation where I've been able to confirm with Wowhead the zone is spider-free: (c) for spider-based critters and (b) for spider-based beasts.
1-60: Azeroth Proper
From levels 1–10 do Eversong woods as you've done (b, c). And you're right to go to Azshara from 11–20 (b, c).
For 20–25, you can't escape spiders: every zone for the level range (Ashenvale, Duskwood, Hillsbrad, and Wetlands) has tons of them. I'd try to milk Azshara as long as you can, then move to Northern Stranglethorn shortly thereafter. If that doesn't cover it, you'll have to do one of the two dungeons—both spider free—for this level range:
If you do go the dungeon route, use the Dungeon Finder tool: getting to Gnomergran as a horde is a bit difficult, and a trip to Scarlet Monestary will require going through Tirisfal Glades, which does have spiders.
Northern Stranglethorn is the only zone in the 25-30 level range that doesn't have spider-based beasts, but it has spider-based critters all over the place. (b, c). If the critters are a problem, you'll have to do a dungeon again. Your only option in this case is Maraudon (b, c).
For 30–35, Southern Barrens is spider free (b, c). Like Northern Stranglethorn, the Cape of Stranglethorn is free of spider beasts, but not spider critters (b, c). Desolace is okay if you stick to the mainland, but an island off-shore has spider critters (b, c). Avoid the Hinterlands like the plague, though.
For 35–40, Feralas is the best bet (b, c). Dustwallow Marsh is infested, and Western Plaguelands has a nest of them to the north. Keep in mind Feralas has Silithids to the south, however.
Choose Thousand Needles (b, c) from 40–45 (more Silithids at the south end of what was once the Shimmering Flats though), then either Felwood or the Badlands for 45–50. I'd personally opt Badlands as there's less green stuff that could be mistaken for a creepy-crawly.
For 50–55 it's Un'Goro crater (b, c). You'd think Winterspring would be a sure thing with all the snow, but Blizzard had to go and create snow spiders. Like Feralas and Thousand Needles, there's a Silithid infestation towards the south if that isn't your bag.
Rounding up the old world from 55–60, it's a bit of difficult one. Blasted Lands has spiders, but your alternative is Silithus. Silithus. You can start the Outlands at level 58, so do that. From 55-57, either finish up Un'Goro or do another dungeon: Blackrock Spire (b, c) is your only spider-free option for this range.
60–70: Outlands
Avoid Terokkar Forest and Blade's Edge Mountains at all costs: they're swarming with spiders. Otherwise, you can follow normal progression:
70-80: Northrend
In Northrend, you should be mostly okay as long as you stay away from the dungeons, which have spiders in them (especially the Nexus, Naxxramas, and Azjol Nerub).
80-85: Cataclysm
If you want to avoid spiders, Cataclysm is not a nice. Only two zones—Mount Hyjal and Vashj'ir—are spider free, making it next to impossible to get to 85 without dungeon crawling. So, I'd suggest doing
85-90: Mists of Pandaria
For Mists of Pandaria, you're directly in bad luck: Jade forest has spiders when doing the jade serpent questline and right after reaching Dawns Blossom, now, you normally reach level 86 around the time you're ready to transition to Dawn's Blossom from the Hozen part.
After that, you need to ride manually from the Hozen place to Valley of the 4 winds. You will start to encounter spiders during the Halfhill quests, so once you reach that, you can head over to the Krasarang wilds quests. there are no spiders during the quests themselves, but there is a whole bunch of them at the far east end. there are no spiders during the hidden master questline.
Kun'lai summit and townlong steppes are mostly safe. Don't even think about Dread Wastes: you need to deal with them during the very first 2 quests. However, there's a tall wall next to the spider nests. In theory, you can ask your girlfriend to place her character on top of the walls, send her to another room, kill the spiders yourself, skin them (to get rid of their corpses) and then let her quickly enter the area. there are critter spiders, but not much you can do about those except polymorph them with the crittermorph glyph.
I could link you the relevant WoWhead pages. However, early on, there was a bug where certain spiders would get evade bugged and follow people to other zones. these spiders show up all over those zones, but aren't actually there (they're in an optional dailies area in the max level zone), just polluting the data and making it unreliable.
90-100: Draenor
Draenor fortunately only has a limited amount of spiders. However, unfortunately some of them are in Frostfire Ridge, the starting zone for Horde. There are 2 major areas to avoid: the cave to the north of Wor'Gol, and the eastern ridge of the canyon to the east of the Horde garrison. Neither of these quests are required to complete the zone.
Gorgrond is close to spider free, with only one bonus objective having spiders.
Talador is again mostly spider free, with the only spiders being located in a small quest hub to the southeast of auchindoun.
Spires of Arak had no spider NPCs, and neither does Nagrand. Tanaan Jungle has some spiders to the north of the Horde base, and some in a cave that only houses a couple of rares and treasures.
100-110: Broken Isles
There are some fel spiders in Faronaar, but you won't need to do anything with them unless you're a Paladin. Apart from that, there are some fel spider critters in the eastern area of Aszuna, but that quest is optional.
There are some spiders during a sidequest in Highmountain that's again optional.
There are some spiders in Suramar in some of the caves, and if you want to complete the Suramar Nightfallen questline, you'll have to face at least some of them.
Apart from that, there are a couple of spiders that don't have a location listed on Wowhead. These are from the Tangleweb breed and I can't remember where they can be found.