The correct lower is a A1-style lower for most builds, though for a more modern build a modern lower is fine.
If you are fortunate enough to own a registered M16A1 lower, or can afford one, then that is the perfect base for the build. For most, the more affordable/convenient option is either an early Colt commercial lower (collectible and somewhat expensive) or a NoDak Spud retro A1 lower, engraved appropriately with a horse-type marking, Star of David, auto selector marking, and and engraved “third pin” marking.
Grey parkerizing was standard, but many lowers were later coated black.
For a carry handle upper, the best configuration is an A1 upper. There should be a teardrop forward assist, but no brass deflector. Rear sight is adjustable for windage but not elevation. Ejection port cover is early style, or can be replaced with the PEC cover. These can be found surplus, or can be obtained from NoDak Spud.
A C7-style upper can also be correct, though not as common. This is the same upper as above with A1 rear sight, but with the addition of a brass deflector. The C7 uppers can be purchased from Fulton Armory.
A2 uppers with brass deflectors, round forward assists, and elevation adjustable rear sights are much more uncommon, but examples are seen, so they are not incorrect.
Flat top uppers are now used heavily by special forces units, and have been finding their way into use by regular units as well.
Color of upper and lower do not have to be an exact match.
The original Colt rifles shipped to Israel were 20″ barreled Colt 603 M16A1 configurations. These were exported from the US to Israel at various times. Most IDF M16s have their origins in these rifles, but have been modified, upgraded, or rebuilt over time. Many of the original 20″ barrels were cut down to build carbines. Other barrels were purpose-built and added as replacements.
For a Rifle configuration, a 20″ lightweight barrel with A1 flashhider and A1 front sight base is correct. These barrels can be found surplus.
For a carbine configuration, especially with a carry handle upper, the proper barrel is usually a cut-down 20″ barrel or a lightweight profile replacement barrel. To replicate this, you can cut down an A1 barrel to 13″ if you are willing to SBR the rifle, or to 14.7″ if you prefer to pin and weld the flash hider. This gives you the correct barrel to replicate a cut-down barrel, but you are also stuck with a 1/12 twist.
The replacement barrels were 14.5″ lightweight profile barrels, and then, later, 14.5″ M4 profile barrels. You can purchase 14.5″ barrels in both profiles and SBR the rifle, or you can try to find a 14.7″ barrel or find a way to shim the flash hider or get an extended flash hider on the 14.5″ barrel and blind pin and weld the flash hider.
If you prefer to avoid the hassle of NFA registration or of pinning and welding a flash hider, then just get a 16″ lightweight barrel – it will look a bit long, but will be less hassle.
Some units use rifle with barrels even shorter than 13″, so if you are into the SBR thing, a 10″ or 11″ barrel looks cool.
Keep a lightweight barrel on a carry handle upper. Flat top uppers look fine with either a lightweight barrel or an M4 barrel, but don’t but an M4 barrel on an A1 or A2 upper.
Use a surplus flat slip ring, although you can use a delta ring with a flat-top upper and M4 barrel.