Compared with other rifles or shotguns, the AR 15 requires relatively few specialized tools. I ended up building one from scratch and rebarreling a problematic upper. If the upper is assembled AND headspaced with the bolt, then the lower is a piece of cake. Castle Nut wrench, a center punch for staking the castle nut (assuming adjustable type stock), some long needle nose pliers, and a set of roll pin punches. A Robogrip or similar wide wrench with good padding on the jaws also helps on starting small roll pins such as the trigger guard. A cheap set of files and pool chalk can also help if a specific problem such a burr in the magwell happens. Of course you also need a hammer for the center punch but is not normally otherwise needed. However, a small soft faced hammer--nylon, rubber, etc. can be used to good effect judiciously.
Oh, and one last thing, buy an AR 15 assembly manual--see Amazon (yeah I know YouTube videos exist--the problem is figuring out which are useful--some information put out there is a) dangerous, b) foolish, and c) ill-advised, and d) risk damage to your components). I use manuals with good pictorials and tips that can rest beside you at the bench and are indexed. This is my personal choice. At my workbench, I do not want a computer, smartphone, tablet, because of risk of damage--furthermore, often I waste more time viewing the online video than I would simply turning to the page needed.
If you are a visual learner instead of reader, then get a dvd or other visual information from the American Gunsmithing Institute (AGI) or some other authoritative source such as a working gunsmith rather than reliance on the quality of You Tube videos. You Tube videos can be useful but you need a sufficient knowledge base to evaluate whether or not the information is useful in the first place. Use an authoritative source first either manual or video and then watch to your heart's content.
One minor tool is a gun oil precision applicator with the long slender metal tube filled with the gun oil of your choice. The lower receiver tends to get dirty and collect crud--the easiest is blow out with compressed air what you can and then hose it out with something like gunblaster solvent and the like. After doing so, you will need to reapply oil to the working parts of the lower. A small drop or two is all that is necessary thus a good applicator helps. You can use the small plastic tubes that come with some oils but I tend to misplace them as it is difficult to store the oil with them attached.
Eventually, the Peace River or Wheeler upper receiver clamp for a vise helps significantly with upper receiver work and cleaning and I can also recommend the Magpul magazine well vise tool especially for quick and dirty jobs. The Magpul vise block secures on the barrel extension rather than putting pressure on the upper. Not crazy about the plain upper receiver blocks that use takedown pins only for securing--if not careful you risk ruining a receiver if not careful. For barrel work, you will need a good solid barrel wrench--don't go cheap here. A standard, well secured, cheap 3-4 inch jawed shop vise is always useful--do not need a wilton but the cheapo harbor freight is more than sufficient--some woodworking vises that are secured can work as well.
If you build a lot, then specialized tools exist to help you--get a Brownells catalog (cheap and informative) and then you can figure out whether you need a specific tool. Good luck.