By far the easiest way to build one is to by a kit. What you are going to see on the market is M16A1 kits. These will have a forward assist, fixed carry handle and windage adjustable only rear sights. Cost is going to be directly dependent on how accurate looking you want it to be.
I personally don't like the look of the early uppers on a late type lower unless the builder goes to the effort to match the lower to the early Colt grey that these rifles came in originally.
To be
correct, a early build should have a A1 style lower of which there are three styles.
A. Earliest is the Model 601/602 (AR15) style which have slab side lowers. These have no fence around the mag release and no forward assist. These came with the three prong flash hider.
B. Next is the Model 603 (M16E1). Early ones have a partial fence around the mag release, but will have the forward assist. They also had the three prong FH
C. Late Model 603's (M16A1) will have the forward assist, full fence around the mag release and the birdcage flash hider.
Last of the fixed carry handle models is the Model 645 has a fully adjustable rear sight, government profile barrel, forward assist and shell deflector. This is the M16A2. These also have the late type reprofiled lower which is the type we see most often today, as well as round handguards.
These are from my collection:
M601/AR15
M602/M16E1
M603/M16A1
M645/M16A2