I am planning to purchase/build my AR-15(although I do hear a little voice occasionally whisper "AR-10"
).
My son and I 'built' our first centerfire rifle - an AR15 - last winter. It was the best project ever. So much so, in fact, that I just ordered three more lowers.
Which companies make good AR-15 components without breaking the bank?
I'll throw out Palmetto State Armory... Their order-to-delivery times can be pretty long, so make sure to read the fine print on the page before ordering. That said, everything I've dealt with them on has been as promised. From a quality-for-the-money standpoint, they seem excellent. Granted, I'm new to this so I can't compare to a lot of other manufacturers. But what I have seen for comparison (Spikes, RRA, BCM, and other cheapos like DelTon, CMMG, etc at the range) has been very positive.
Any particular websites you'd recommend for reviews, research, or purchases?
As has been mentioned, AR15.com is a wealth of knowledge. The tactikiddies can be a little over the top there, so just be aware.
Google is your friend. The AR15 is such a popular and prolific platform that there are tons of good resources out there. I find most of my 'answers' by searching for "AR15" plus whatever questions I have. I then prioritize the sites I read to the major gun sites and cross-reference to ensure accuracy.
Is there a compelling reason to buy the complete uppers/lowers or to build piece by piece?
We built our lower. Compelling reasons? Well, price and fun. If you're willing to be patient, you can snipe components on sale and, IMO, save quite a bit. More importantly, it's just fun. My son and I had a blast putting our first lower together. We don't have a toolbench, so we did it after his normal bedtime in the kitchen. Such fun!
This video was invaluable to us:
http://www.youtube.com/watch?v=iA_Vkb2UB1w
We bought a completely built upper. While there might be a price savings and fun factor to be had in hand-building, I thought the potential performance and safety issues that could be created by a imperfect build (remember our kitchen?) justified buying an upper built by professionals.
I'd be happy to respond to any PMs if you have other questions. For the record, we're playing with .223/5.56 only, so I won't be much help re: your caliber questions. There are many others who will be, though.