Well, I would always recommend buying used parts if you don't have much to spend. You can get quite a nice discount and many of the parts you'll get will be in great condition.
Second option would be to use the bike builder at webcyclery.com. When I bought my trials bike through them and used the bike builder it wound up saving me about 10% compared to if I had bought all of the parts seperately. Not only that, but their service is unmatched, not even my local bike shops are as nice and friendly as these guys.
I realize you don't have a lot to spend, so I would probably cheap it a bit on the frame. Check out a zoo or an echo. I wouldn't cheap it on the parts that matter and the parts you will be keeping around for years, going from frame to frame.
Rear wheel: or at least the rear hub, spend a lot of money now, or spend a little now and then a lot later. You will end up upgrading eventually, and it seems stupid to buy a shimano now, then replace it with a King when it's freehub breaks in a few months. Then you'll be replacing the hub, spokes, nipples, and if you don't build your own wheels, you'll be paying for labor again. A king or profile hub will likely last your entire trials career. As for the rear rim, check out either a Planet-X BMF (the EXACT same rim as a DX32, just with brass eyelets), an Alex DX32, or a try-all rim. Only get the try-all rim if you are running a magura hs33 in the rear, it is highly unlikely that it will work well (or at all) with V-brakes.
Cranks: FSA power pros will likely last you a long time if you make sure you keep them tight on the bottom bracket, and the pedals tight in the crankarms. You could eventually upgrade to bonz or middleburn at a later date if you decide you want something stiffer or lighter.
Pedals: Sun Ringle pedals will get you by for cheap, and if you can keep on top of replacing the pins when they need it, you won't have any problems with these whatsoever. A cheaper option would be to go with some VPs, but don't expect them to last much more than a month. A more expensive option would be to check out some Atomlab aircorps pedals (NOT the clear plastic lexan bodies). I absolutely LOVE mine, and will never ride another pedal. These should last you virtually forever and they're completely rebuildable. What do you want to stray from? Odyssey Triple traps, I will just flat out say DON'T BUY THESE!
Bottom Bracket: A cheapie square taper shimano should do the trick (provided you buy square taper cranks). It will probably break on you eventually, but I'd bet it will get you through the sport class without any breakage, provided you aren't regularly going large.
Handlebars: Pick up a try-all bar and you should be pleased. You can spend a bit less, but why bother when you're talking about minimal savings? Another benefit of this bar is its standard 25.4mm diameter, so you can run normal stems.
Stems: Another vote for try-all parts here. Not too expensive, but it should last you a long time. Stems are hard to recommend because most stems are only available in limited sizes, and what size you want will narrow down the field of choices DRAMATICALLY. You can always depend on a thomson stem though, and they come in about any size you could ever want.
Forks: A Planet-X superlight fork is pretty cheap and should hold out pretty well for you. They're really too new to be sure about that, but I'd wager a bet that they'll be pretty dependable. Other options for light and pretty dependable would be either an echo or a zoo fork. Koxx forxx are nice, but they're too damn expensive at $230.
Front wheel: Always make sure you get a hub that has disc mounts even if you aren't planning on riding a disc. You never know what you will be doing in the future, especially because it sounds like you're just beginning in this sport and your tastes will change a LOT as you gain more experience. That being said, about any front hub will work for you, but according to your budget... and this would be a good place to skimp a bit. As for the rim for the front, if I was on a budget I would pick up a rhyno lite because they're cheap and a pretty good width so your tire won't fold too much. If you want lighter, you're probably looking at a mavic XC rim and then your tire is going to be folding on natural... everything's a trade off.
Brakes: I can always recommend XTR levers, they just feel great. If you don't want to spend that kind of money, check out some cheap avid levers. For the front brake, I'd say an avid mechanical disc brake, almost any V-brake, or an hs33 will work just fine. The avid disc will work well in almost all conditions, but you can save money and go with a V-brake here. I would only buy an hs33 for the front if you can't stand the feel of cable brakes. For the rear, I'd have to say either get a V-brake, or an hs33. A V-brake will have more holding power in my opinion, but if you order a frame with 4-bolt mounts, then get an hs33. If you order a frame with V-brake studs, I'd probably get a V-brake, because hs33s don't perform as well and are harder to set up on V-brake studs.
Brake pads: My favorite are the koxx bloxx pads for hs33s. for the avid mechanical, the stock pads should work perfectly. Another option to the koxx bloxx for the hs33 would be plazmatic CRM pads. They don't grip quite as well in my opinion, but may work better than the koxx bloxx if you're riding in cold weather a lot (not likely in CT). For V-brake pads, get either the plazmatic CRV pads, or koolstop salmon pads. The CRVs will hold better, but are a lot more expensive, buy as your budget allows.
Grips: I can ALWAYS recommend ODI ruffian grips with the ODI clamps. I won't recommend anything else, because I think it is worth the extra money for these grips... I love them.
Headset: It's always nice to have a king headset, but since you're on a budget, check out the FSA pig headset. You shouldn't have any problems with these, and they're much cheaper than a king.
Tires: I haven't ridden maxxis tires and don't know which ones to recommend, Kevin (WhiteRavenKS) can fill you in on these. If you don't want Maxxis or want something that will last longer, get a michelin. I'm pretty sure michelin tires last a bit longer than the maxxis super tackys. I run a michelin comp24.1 2.2" tire front and rear and they're heavy, but so worth it in my opinion. If you want to save weight in the front, get a hot S, but don't skimp on the rear tire, get something hefty and ONLY a michelin (comp24.1 2.2" or 2.5") or Maxxis (I'll let Kevin recommend his favorite).
Chain, cassette, chainring: You can get by with a cheapie-ish rear cassette, like a shimano or sun-race, but you should get something with either an 18 or 19 tooth ring on it. For the front chain ring, a 22 tooth blackspire chuck granny gear will do it. For the chain I would NOT skimp, too much depends on this. Get the SRAM PC99 or a rohloff trials chain, nothing else will do.
Derailleur, shifter: If you get an 8-speed cassette you will want an 8-speed shifter. Any shimano derailleur will work with them, it's the shifter that makes the derailleur compatible with either 8 or 9 speed cassettes. I don't like grip shifters (like SRAM) so I don't know much about them and hence... won't recommend anything from SRAM. It's not that they're bad, many like them more and will surely recommend some SRAM stuff to you (Brett McCullough may weigh in on this). A shimano sora rear derailleur will work just fine on a budget, and the cheapest shimano shifter will work just fine too.
I THINK that covers about everything, but there could definitely always be some parts I'm leaving out so if you have any questions about parts I did or didn't mention, just ask and I'll tell you what I think.
Also, if you do purchase from webcyclery, let them know where you heard about them. I am sure they like to know their advertising dollars are well spent.