Note that this has been edited to reflect the changes in Cataclysm / The Shattering, so the stat weighing is not final and a proper raid-balance of stats is not concrete.
Int provides you with spellpower and a larger mana pool, so it is naturally a strong stat.
Haste is also important, as it allows you to cast your spells faster, and to an extent, reduces the GCD (which makes a difference for instant cast spells). You get a good amount of haste passively through talents though (9% through Judgements of the Pure, 3% through Blazing Light, plus flat cast reductions on certain spells).
Crit is always nice to have, and it synnergizes nicely with some talents (Crit Holy Shocks reduce cast time on HL / DL, for example).
Mastery (at 80 and beyond) gives your heals a bonus shield equal to a % of the heal amount on your target. Shield effects have always been quite effective, and this more or less gives you a permanent Valan'yr effect to work with. I can see this being a very popular mastery, however we'll have to see how well it scales further on.
Spirit is now the go-to stat for mana regen as of The Shattering, and will continue to be so throughout Cataclysm. There may be a FEW items / enchants out there that provide MP5, but for the most part you're looking for spirit for your regen needs. It still remains to be seen just how much spirit is going to be needed to sustain throughout hardmode fights (especially with the ability to Judge Seal of Insight AND Divine Plea as decent mana regen abilities), but regardless, Spirit is the new regen stat.
As for leveling, just worry about Int, Crit, and to a lesser degree, Haste. Early on and leveling, a lot of healing will be done with Holy Shock and Word of Glory, which are both instant. Haste wont play a big role until later when you need to utilize your Flash of Light/Holy Light/Divine Light spells a bit more.
Average used bandwidth is very low. I haven't tested it recently but it used to be possible to run WoW off a 56kbps dial-up link, implying a download rate of probably 6kBps or lower. The latency tends to be a much greater issue, as creatures/players may not be where your client shows them as and it can impact upon spell casting delays, etc.
By the way, if that connection really is 256 mbps, that's faster than almost all of Australia and New Zealand plays WoW at - that is 32 MB/sec, and we tend to top out at 10-20 MB/sec.
Best Answer
There are multiple types of currency available in World of Warcraft, in addition to gold. Each currency is earned a different way.
Current currencies
This section deals with currencies that are "current" as of the latest expansion - Mists of Pandaria.
Gold
Gold is the primary currency used for buying items from most vendors and from the auction house. Gold is tradable with other players in game through the trade window and can be mailed to other players by using a mailbox. Gold is earned by killing enemies, selling items, etc.
For more information on how to get lots of gold, see How can I earn lots of gold?
PvE points (Justice and Valor)
Player vs Environment points are split into Justice points and Valor points. These points are earned by killing bosses in dungeons, raids, and as a reward for using the dungeon and raid finder. These points can be spent at Justice and Valor vendors for relatively high end PvE gear.
PvP points (Honour and Conquest)
Player vs Player points are split into Honour and Conquest points. These points are earned by killing players in battlegrounds, arenas, and cities belonging to the other faction. These points can be spent at Honour and Conquest vendors for relatively high end PvP gear with resilience on it.
Questing currencies
Darkmoon tokens are earned by taking part in the Darkmoon Faire and can be used to purchase items from Darkmoon Faire vendors.
Lesser charms of good fortune are earned by completing Mists of Pandaria daily questions and used to purchase Elder charms of good fortune.
Elder charms of good fortune are used to "re-roll" on items that drop in Mists of Pandaria raids, to provide you more opportunities to get epic loot from Tier 14 bosses.
Timeless coins are earned from completing quests on Timeless Isle and are used for the purchase of relatively high end epic gear.
Mogu Rune of Fate are purchased using Timeless coins and are used to "re-roll" on items that drop in Mists of Pandaria raids, to provide you more opportunities to get epic loot from Tier 15 bosses.
Notable currencies from past expansions
Tol Barad Commendations area earned by completing daily quests and the Tol Barad PvP map and can be used to purchase a variety of items including low level items for level 85 characters, mounts and pets.
Marks of the World Tree are tokens earned by completing Molton Front daily quests and are used to purchase items and to progress through the Molton Front story line.
Mote of Darkness are tokens earned by killing bosses in the Dragon Soul raid, used for purchasing crystalline geodes (which contain high end Cataclsym gems).
Essence of Corrupted Deathwing are tokens earned by killing Deathwing in the Dragon Soul raid, used for purchasing elementium-coated geodes (which contain high end Cataclysm gems).
Illustrious Jewelcrafter's Token are tokens earned by completing jewelcrafting daily quests in your faction's capital city, used for purchasing Cataclysm jewelcrafting recipes.
Dalaran Jewelcrafter's Token are tokens earned by completing Dalarn jewelcrafting daily quests in Dalan, used for purchasing Wrath of the Lich King jewelcrafting recipes.
Champion's Seal are tokens earned and spent at the Argent Tournament grounds.