An AK kit without a bbl is one of the harder ways to go about building one. With the original bbl included, the kit assembles fairly easily as the whole thing was once an assembled rifle that was cut up. Those kits are expensive for a reason.
A stamped receiver AKM rifle with a muzzle brake has 6 parts that need replaced to be 922(r) compliant. Assuming you use a US made receiver, that leaves 5 parts. A trigger group is 3 parts, so you have 2 left. A US muzzle brake is cheap and easy to replace, as is a pistol grip. Gas piston is also easy and cheap, a good choice on some rifles where US made external parts do not match the originals too closely.
Bbls, you have two choices: a new US made one (one 922 part right there) or a foreign made one, either an uninstalled new bbl or a used/new one from an assembled rifle. Most of the new bbls of either type are basically profiled blanks, you have to position and pin on all the components such as rear sight block and gas block, also drill the gasport hole. Advanced gunsmithing here. The ones from an assembled rifle are easier in that all the hard work is done, but it still needs headspaced when installed, as do the new bbls. This requires a set of headspace gauges and on previously assembled bbls, usually an oversized bbl pin and a drill or reamer to make the hole match.
In addition to the rivet kit you will need rivet setting tools. All can be homemade out of either a cheap set of boltcutters or scrap steel.