So, the absolute first thing that I would spend money on is a pair of rings. Specifically, if you can get your hand on two rings with the Wounding property (with +2-4 Damage on it) as soon as you reach level 6 (which should be the minimum to equip them), you'll notice a dramatic increase in character power. These two rings will cost somewhere between 3500 and 4500 gold, depending on the exact properties (a Scouting Ring of Wounding, with +Magic Find as well is a particularly great grab). Of course, the vendors inventory is random. Fortunately for you however, it refreshes every time you exit the game and create a new one. Once you've rescued Deckard Cain from the cathedral (which is the prerequisite to access the vendor in question), you should log in and out a few times while checking the vendor. Once you see a ring that appeals to you, snag two of them, and you're good to go.
After that, The Blacksmith is probably your next priority. Specifically, you'll want to make sure that you always have him trained up to produce gear either at or just above your current level. That means you'll want to have pumped 8,000 gold into his training by level 10, another 20,000 by level 20, and so forth. You can keep track of all the numbers, as well as the recipes available at each tier over on Blizzards site.
Assuming you're keeping the blacksmith current, at this point, any additional gold can be spent as you please on upgrading your equipment. Whether you do that through crafting, the auction house, or browsing the various shops of Sanctuary, is your call. There are advantages to all of them, and at this point, the game opens up enough that one-size fits all answers are no longer easy to provide. Just remember to keep your artisans (the Blacksmith, and eventually, the Jeweler) up to date, and you're good to go.
And whatever you do, don't worry about the Stash unless you're at the point where you have more gold than you have uses for it and the convenience is suddenly of value to you. Don't expect that to happen anytime soon though.
Below level 60, there's none, apart from farming areas with many monsters in them.
However, at level 60, the most effective way should be to do "extended boss rushes":
First you have to know that Blizzard has actually implemented mechanics to balance drops so that purely farming bosses isn't more effective in farming for rares than it is to farm areas with normal monsters/champions, namely the Nephalem Valor Buff .
The original quote from Bashiok is this (although the thread containing it has since been deleted):
You will not be farming bosses. Bosses won't drop the best loot, they won't even drop really great loot. Part of Inferno and our intent with getting people out into the world and hunting and killing lots of different things is putting the best loot on rare and champion packs, and the great thing about rare and champion packs is they have random affixes. They're like a box of chocolates. Murderous, snarling, blood-soaked chocolates. You're not going up against a boss where you know "Build A" is the best way to minmax against it because it has abilities and resistances X, Y, and Z. What is the best build vs. an "Arcane Enchanted, Teleporter, Frozen, Knockback" skeleton pack? Got that figured out? Cause it's not going to be the best against the next pack you come across, and you're going to want to kill that one just as much.
However, there's something extra to this: There's no official word form Blizzard about this (yet), but as many players (among them, me) are currently experiencing, it strongly looks like major bosses (such as the Skeleton King and The Butcher in Act 1) have at least two guaranteed rare-drops as long as you have five active stacks of Nephalem Valor. "Strongly" means that I have done about 10 runs on the Butcher so far and he has dropped two or more rares (along with a higher-than-usual amount of magic items) every single time.
This means that probably the most effective way is to get five stacks of Nephalem Valor as fast as possible, and then farm a certain boss in the Act that you're playing.
Best Answer
At the end of the season the character you created becomes a normal character in your list of characters. All items in the season stash will be sent as mail, there is a blue post on this here: http://us.battle.net/d3/en/forum/topic/13922512563
And as for the paragon levels and experience earned in the season
I also found this blog containing answers about seasons ending by a blue user who answers many of the post season questions if this answer doesn't satisfy all of your curiosity. While it is mainly about how it was handled in the ptr, that is essentially the same process that will be used at the end of season 1 now.