BEFORE YOU BUY ANYTHING, read up about it. There are instructional DVDs and books out there. Research first. Prowl the web. Check out AR related forums. AR15.com is a good place to do research, but there are dozens of sites out there.
Next, you need to know what is legal in your state. Know the restrictions and stay within the limit of the law. Anything marked as "NFA Rules Apply" means it has to go thru an FFL and you need paperwork for it (SBR -short barreled rifle or AUTOs). You can have a barrel less than 16" long without extra paperwork with the ATF (if it is even legal in your state) if you build an AR-15 PISTOL...but if you attach a buttstock to it, you have jsut created an unregistered SBR. A definite no-no.
Go to gun stores, gun shows, and pawnshops (if they allow FA sales from pawnshops in your state/city), and ask to hold everything. This will give you an idea on where to start with your first build, in terms of barrel length and profile, handguard type and style, upper type (flat-top, high-rise, or with carry handle), pistol grip style, buttstock type and style, and even color. Touching the guns doesn't cost you anything, but the feel of it will stick in your mind.
Decide on the caliber. Most ARs out there are chambered for .223 Remington or 5.56x45mm NATO Standard. Know this: you can safely shoot .223 Rem in a 5.56x45, but not the other way around. Like in a .357 Magnum, you can shoot .38 Special; but you cannot shoot .357 ammo out of a .38 Special revolver. I always recommend building with parts designed for the 5.56x45mm NATO round, they tend to be more robust (to take the higher chamber pressures, among other things). The lower receiver will be stamped with the caliber that receiver is intended to be used with. Tracers and AP (armor-piercing) ammo will typically be 5.56 NATO, and can be had (if legal in your state) from online retailers or local gun shops or gun shows. The .223 Rem you can buy at Walmart!
Then buy your assembled lower, from a good manufacturer (DPMS, COLT, OlyArms, RRA, and others mentioned here). If you are feeling adventurous, buy a stripped lower receiver (about $200 or so out the door) (NOTE: the lower has the serial number, and you need to get it from an FFL; everything else -depending on where you live- can be mail-ordered and shipped USPS) and a quality lower parts kit (I almost always use DPMS lower parks kits, manufacturing quality is consistent). Go over your book or DVD again. You can find exploded diagrams with parts labels all over the web. Know the parts and their function and where they go. Then buy (or borrow) a set of pin punches (ideally brass) and a small hammer (like a watchmaker's hammer). Although you should have things like roll-pin punch and the takedown detent pin installation tool, and barrel blocks and receiver vice blocks, you can make do (for now) without by being very VERY careful. Go slowly. It's not that hard. With quality parts on hand, I can fully assemble a lower receiver in less than 20 minutes while watching TV and never need a bench vice.
If you will use a collapsible buttstock, you will need a buttstock wrench, otherwise you risk damaging the parts. Be careful with that danged buffer-detent pin and spring as well as the obnoxious buffer spring! If you are planning on having a long and heavy barrel (such as you would need for really accurate shooting or hunting), plan on having a standard A2 buttstock (sometimes called an E2 buttstock), preferrably the one with an empty void for the buttstock counterwieght, otherwise your rifle will be so front-heavy that it will be very difficult to manipulate and aim without a bipod.
If you plan on building your barrel assembly, you will need a barrel block and barrel wrench. No way around that. For beginners, I recommend buying a fully assembled upper with barrel headspaced and test-fired. OlyArms (Olympic Arms) and RRA (Rock River Arms) make very good, affordable uppers. If you plan on redoing an installed free-float handguard tube later on, you will need a small propane blowtorch and Loctite Red as well. It's a hassle and takes muscle. You will need to know what HEADSPACE means, and have (at minimum) a "no-go" gauge or both that and a "go" gauge. With a standard sight tower (the triangular tower above the muzzle), you will need a Front Sight Alingment Tool; flip-down sights or BUIS (Back-Up Iron Sights) have a screw adjustment and need no special tools. Chrome-lined barrels are OK for longevity (they resist chemical corrosion better than unlined barrels) but accuracy suffers, but offer better bullet "lubricity" and (to me) are easier to clean. I will not build a competition- or hunting-grade upper with a chromed barrel, because accuracy is paramount for this application. For plinking, chromed is OK as far as I am concerned.
Handguards generally only come in 2 sizes: rifle and carbine. If your barrel is 16", it is carbine. If over 16", it is rifle. With the exception of "free-floating" handguards, on plastic two-piece handguards you do not really need tools to change handguards, you just need to know how. This is very easy.
The beauty of having an AR-15 is the plethora of parts and accessories available out there! Your first AR build will be exciting and produce a unique firearm. The joy of building it is surpassed only by the joy of shooting it. You can have or build an all-black rifle, or get combo colors (usually desert tan or light olive green), or even paint it yourself (research DuraCoat) to personalize it further. You can customize to your heart's content, later on. Add a foregrip. Add a rail adapter (if it doesn't have one). Add a laser, add a weapon light, whatever! If you get a flat-top upper (no carrying handle), you can have your choice of detachable front and rear sights with optics (scope, red-dot, whatever!) or even a detachable carryhandle with rear sight built in (works best with a barrel that has the front sight tower). If your upper has a carry handle built-in, you can get a rail adapter to mount a scope or other optics on it (look at the pics of the first two ARs I built).
BEWARE that it is (relatively) easy to convert an AR-15 into an M-16 (full auto). Doing so without ATF paperwork or approval is a Federal offense. Mere possession of a part for a full-auto without proper approval and paperwork is a crime. If you just have a full-auto hammer or even just the bolt carrier in your parts drawer, in a ziploc bag, it is still an offense. You CAN legally adapt your AR-15 to be a "rapid-fire semiautomatic" (an "automatic" fires multiple rounds as long as the trigger is depressed; a "semiautomatic" will only fire one round for each trigger press; a "select-fire" weapon is a full automatic capable of single-shot-per-trigger-press or multiple-shot-per-trigger-press; and a "burst fire" is an automatic that will or can fire only three rounds for each trigger press as well as full-auto as long as the trigger is pressed and semiauto fire). For rapid-fire-semiautomatic, research the Tac-Trigger, and Youtube "bump-firing" (this is unsafe, I do not recommend it, because the rounds fired are not aimed, but others enjoy burning thru ammo...go figure).
Do not be afraid. Millions of civilians have done it, there is no reason you can't! And have fun!