If you can change a lightbulb or screw in a screw, you can build an AR 15. You will need a good action block, and a good armorers wrench. Other than that, you probably already have some pin punches, and other tools that will come in handy.
All the expertise in the world is right here should you get stuck.
There are a few tools I'd recommend, but you don't *need* them.
I picked up a basic bench block from Brownells, and a set of roll pin punches and roll pin starter punches, along with the front pivot pin tool. They make life very easey, but you don't have to have them, lots of guys here do it without them.
To build something that won't break the bank, I'd go with an Ameetec, Stag, or Mega lower...you can usually get one of those for around $85 plus shipping.
If you can actually buy direct from BM and not pay an FFL transfer fee, that might be an option...but BM lowers are a lot more expensive than the ones I mentioned, I believe.
After that, you can mail order anything you want, and have it shipped to your house.
You might consider a kit from J&T or Model 1 in the configuration you like. It will contain everything you need to build a complete rifle except the lower receiver, which is the actual firearm.
I've done 2 with Model 1 and one with a J&T kit. J&T is better fit and finish, but all 3 go bang when I pull the trigger. I had a major problem with the 2nd Model kit...gas block issue...and they took care of it pronto. Others have had worse luck with their customer service, but I didn't.
You can always cruise the EE looking for parts as well. You can usually find barrels, handguards, and anything else you need.
With a kit, a basic rifle will be around $550 to $600. If you pimp it out with a railed forend, flip up sight gas block, and stufff like that, you'll bump it up to around $800 or more depending what parts you use.
I've had very good luck with Yankee Hill tubes and gas block/sights, fwiw. It's much cheaper than the ultra high dollar stuff, and it works fine for the light duty that my rifles see.
I would HIGHLY recommend a flat top upper. Down the road, if you build another rifle, get an A2 upper...but the optics options with a flat top far outweigh those for an A2.