For stat priority I would be looking at dex > all res > vit > crit hit dmg > ias > crit hit chance (so u don't need sharpshooter). Try to get movement speed on boots as well, as a minimum for movement speed. A budget of 2 mil would be quite difficult to get a well geared one, but if u are patient enough and can find some good bargains... u would probably be able to farm A1. For anything from A2 onwards, u would need to invest in some more I'd say.
For skill builds... I personally like hungering arrow with puncture for primary attack, and currently using cluster arrow with cluster bomb for secondary. A lot of ppl use elemental arrow with frost arrow... which I haven't tried yet, but I hear good things about it. For other skills, I'd recommend starting off with Smokescreen (lingering fog), Preparation (backup plan), Companion (bat), and Caltrops (immobilise rune). For passives, it is pretty standard to go steady aim and archery for first 2 passives... 3rd passive can be whatever u like. I'd use grenadier if using cluster arrow... other good options are sharpshooter and tactical advantage. Play around with things and see what u r comfortable with.
You can find a 800-900 DPS magic bow for cheap (10-20k) with Dex and Vit. Magic, not rare.
Build up Max Discipline on the cloak and quiver.
Rare cloak is maybe 300k, with Dex, Vit, 3 sockets and some Max Discipline. Quivers: I haven't been shopping lately but I bought mine early on in Inferno when I had no money (less than 1m), so I might have bought it for less than 100k. Dex, Vit, Crit %, Max Disc.
Boots without Movement Speed are available for like 5k with everything else you need (Dex, Vit, resists). If you want boots with movement speed, you simply sacrifice things like all resistance, and the price does go up. I'm trying to find a way to live without movement speed, because the boots I want are in the 1m+ price range (yes, I know that sounded like Sex In The City...LOL)
Bracers, Belt, Shoulders, Pants, Gloves can all be had for less than 100k, for basic survivability (Dex, Vit, maybe a third stat like sockets, crit damage, resists, etc., whatever you feel is helpful to you).
Jewelry is more expensive but you can definitely get bonus IAS, Dex, Crit % or Crit damage spread out amongst your amulet and rings, all less than 100k.
Over the course of A1, with NV boosts, you should be able to generate some cash. You won't be uber-anything, but you will be able to progress and finish the Act. Once you do, you can farm the Imprisoned Angel quest to the Butcher, and it will get easier and easier.
You shouldn't have trouble achieving 20k DPS (+/- 5k), 40k HP, 150 res, 2200 armor.
I've been using this build successfully throughout Act 1, pretty standard build with only about 8% crit/80% crit damage. As Malicious said above, I tried Frost Arrow after 1.0.3 and much prefer it to Nether Tentacles. If you're having trouble without movement speed boots, remove Sharpshooter and use Tactical Advantage instead.
Act 2 elites are a lot tougher though. Let's cross that bridge when we get there :P