So the first thing you should do is go down to your local gun store to see if they have AR-15 stripped lowers in-stock for delivery or can order you one fairly quick. The thing to look for is a forged aluminum, mil-spec. lower in the caliber of your choice (5.56 or Multi?). The brand is more or less up to you based on what company roll-mark you like. The parts that go into it are more important than the alum. shell that holds them.
The BATF considers this serial numbered item to be the "Firearm" so you will need a federally licensed gun dealer to to do the deal for you. Obtaining the AR lower for you is the only part that you'll need the services of a gun dealer for.
It comes home looking like this:
Alternatively, you can order a lower on-line from a vendor and have your local gun dealer arrange for delivery to his location so he can do the paperwork and do the transfer to you. He will charge a fee for this from $20 to $50 depending on your location & relationship with him. Sometimes this type of purchase will work out in your favor financially, sometimes not.
Next you'll need to get a Lower Parts Kit (LPK):
You can order these on-line anywhere without any problem No license or shipping restriction required.
Installing the lower parts in AR lower is fairly simple and only requires a few special tools to complete like a lower vice block and a castle nut wrench for the buttstock. There are ample instruction and videos for doing this procedure on this site and on many others. I'm assuming you already have hammers, punches and needle-nosed pliers and such.
You'll also need to pickout and order a buttstock setup you like and order it too. The LPK comes with a standard pistol grip, but you may want a custom one too.
When you're done assembling a your AR lower it'll look something like this:
After the AR lower assembly you'll need to pick-out an AR upper assembly that will suit your needs and order it locally or on-line. There are many different brands and types, so I can't offer much help there. Since this is your first AR, I suggest you get a complete upper. It doesn't take any special tools for this and it will probably workout much better for you to do it like this. The thing to watch for is that it should come with a complete bolt assembly and charging handle to be considered complete.
Mating the upper to the lower takes less than a minute and then you'll have a functional AR. Most uppers and lowers will fit together with no problems. Iron sights and / or optics will also be needed to properly aim your new AR. Many, many options there to choose from.
By following these steps you'll end up with the complete AR package.
Hope this will help you on your AR quest.