Grab a comfy seat, this isn't going to be short.
I'd have to go the build route because the retail price for a Bushmaster at $800 is just too high for me.
I'm looking to spend $650 MAX with a good complete upper and good lower.
I'd like my first to be a 20" A3 with carry handle.
What can you tell me? What lower, what upper?
If it's truly $650 max, then you probably won't get an A3 version especially a name brand rifle. An A2 version is doable for about $600 partly because it seems everybody wants an A3 now; lots of A2 and postban stuff for sale. Going much below $600 is tough for a decent AR of any form. The experts do it easily with a mix of used parts, but they have the tools and knowledge to put it all together and what to avoid.
I've been spending alot of time at ar15.com lately especially in the EE (equipment exchange). To get a complete A3 (with carry handle) for $650 is going to be tough although may be possible if you shop very, very carefully. That $650 won't leave any money for assembly tools, so you're really looking to buy a complete upper and a complete lower. $700 would make this MUCH easier.
A decent complete lower will be minimum $200 (with an A2 fixed stock) and $250 if you insist on an RRA, BM, or Colt brand. CMT, LMT, or Stag brands are fine and lower cost. A collapsable stock will add $30-$50 to the lower price.
This (link) is the cheapest I've seen for a new assembled lower and it would be a decent choice if you want a collapsing stock. Lets say you get that assembled lower for $225 shipped. Add in your FFL transfer fee (assume $25) and you're at $250, minimum.
That leaves $400 max. for an A3 upper with carry handle. There are alot of people that would like to buy that for $400 and you're in competition with them all. The removable carry handle will cost $60-$80 easily. The $60 ones will go very quickly, assume $75. That leaves $325 for the A3 upper complete with bolt, bolt carrier, and charging handle. Uppers in this price range (with the bolt group) usually have something less than desirable. It could be they are heavily used or they are a postban model (with muzzlebrake or bare with no threads) or a plain 20 inch heavy barrel (non-chrome lined, maybe postban) or something. They'd sell for more if they were very desirable. There are alot more A2 uppers for sale compared to the A3 uppers.
Just a few minutes ago, I bought a complete A3 upper without the carry handle for $300. It'd been shot alot and used in the outdoors so it has scratches, dings, etc. It also had a 14.5 inch barrel with an AK-74 type muzzle brake permanently attached (can you say LOUD!). The only reason I bought it was because it was a factory bushmaster complete upper assembly. Those are $500+ new. I'll keep the bolt group and upper receiver then sell the barrel assembly back on the EE to recoup some money and because I don't want that loud beast. I'm doing a custom, all-BM, free-floated upper for less than $500. I don't think you can get any new, complete BM upper for less than $520 plus shipping.
Your best bet is going to be somebody who needs to sell a lower, upper, or complete rifle quickly and they price it low. You almost have to live in the EE to catch those deals, but they do happen. Another good possibility is to buddy up with someone local who has the assembly tools and pick up parts over time. ARs just aren't cheap.