80% lowers are not a firearm so they do not require any paperwork to buy or to finish. However, you do need to read up on the ATFE requirements for making once you complete the firearm, but there is no paperwork that needs to be filed unless you sell it. But you do need some pretty specific skills and equipment. To build just one or two is going to cost you more in the long run than buying a stripped lower and just throwing the parts in. Of course, with the stripped lower you do have paperwork to complete.
The 80% lowers are cheap enough that if you mess one up you won't be out much money, but check the price of the buffer tube tap and that eats up much of the savings there, for just one lower. You need a milling machine and various end mills to finish the lower so unless you have all that, you won't have much success. I suppose you could finish one with a file and a drill press but my time counts for something. And then if you want a hard shell on the aluminum you have to pay to have it anodized. And that is not cheap on a per unit basis.
If you are really interested in pursuing this, go over to AR15.com. There are a lot of people over here who have gone the 80% and even the 0% route so there is a lot of information there for you to read up on.
Building up an AR-15 from parts is very easy and safe. That is total BS about it being dangerous and spoken by someone who has no experience at all with building an AR rifle, that I guarantee you. I have built over 20 for person use and while you do need some tools to do it right, there is nothing dangerous about it. Either the gas tube is right or it won't work. It sure as heck will not blow up. If you use the wrong gas tube, then it won't work. It won't blow up and you would have to be a total idiot to use the wrong gas tube and not know long before you got to the shooting stage. The headspacing is set with the barrel extension and bolt and is it very rare that if you buy a new barrel and bolt, even if from different makers, that they will not headspace correctly. I did buy the headspace gauges and every one of mine checked out perfectly. The only time you are even remotely likely to encounter headspace problems is if you use a used barrel and used bolt. Building the AR-15 from parts is one of the easiest and safest builds you can do. Uppers and lowers are very safe to build and assembly. The only thing you really have to watch is the fire control group. With any set of instructions or FCG you buy, you will get instructions for doing the safety checks. The biggest mistake made is putting the disconnector spring in upside down and the gun doubling. That is not good. So make sure you put it in correctly. The other area is not so much a safety thing, but a function concern. Know what the devil you are doing before you do it. A CAR length barrel does not have a thing to do with the buffer and buffer tube you use. If you use a CAR stock then you must use a CAR buffer tube, buffer, and spring. A rifle length stock then you must use a rifle length buffer, tube, and spring. Putting a CAR barreled upper on a lower with a rifle stock is not a problem nor is putting a rifle length barreled upper on a CAR stocked lower an issue, except it looks funny.
If you are interested in doing an AR build, check out AR15.com in the build it yourself section. It is great but you do tend to catch the black rifle disease easily. I figured I would build one, and that was 20 builds ago. There is just so much you can do, from .17 to .50 caliber, and all on the AR-15 platform. And the accuracy you can get out of the AR-15 will rival most bolt action rifles, all but the highest grade match guns and if you compare a match grade AR to a match grade bolt, you will be in for the run of your life. They are incredibly accurate if you do the tricks and use a quality barrel. But don't expect 1/4 MOA from a $150 barrel. It might to MOA at best, and for 99% of us, that is plenty good enough.
And you do save a ton of money doing your own builds. However, out of pocket price is about the same. Where you save the money is you build the rifle the way you want it from the get-go. If you buy a factory rifle it will be no time at all before you want to start changing things, stock, forend, grips, charging handles... and that is where you spend your extra money buying factory.
To build a lower all you need is a three or four roll pin holders, three or four roll pin punches, and two or three steel punches. If using a CAR Stock you need a CAR wrench to tighten the castle nut, about $10 or less. That is all you need to build a lower.
On an upper you need an upper fixture, about $40 from DPMS. The same roll pin punches and holders work for it as well. You need a barrel wrench for whatever forend you use and that runs about $20 on average. A torque wrench is good for the anal but you really don't need one. The most expensive item I can think of that I recommend you getting is a lapping tool to true up the front of the uppers receiver's threads so they will be perfectly square to the upper. That tool is about $35-40. That makes sure that when you put on your barrel and forend, the barrel will be centered and your sights don't have to be cranked way over to get the rifle to zero. I have used this tool on every upper I have done and found all of them not to be perfectly true from the maker, be it an $80 DPMS upper or the $225 VLTOR billet machined upper. ALL of them needed some truing so brand doesn't mean squat. Square up the front of the threads that the barrel extension butts up against and your sights will zero centered and your barrel will be centered in the forend. Don't square it up and you will probably be OK, but if not, that is where your problem is. It is not a dangerous condition though, just aggravating.