I️m new to ARs but I️ just purchased the parts to build one.
Lower: Palmetto State Armory complete lower
Upper: Aero Precision Complete M4E1 upper.

Question: will these two pieces fit together properly?

I️ have the BCG and charging handle as well so I️m good on that.

AR15s across vendors are fairly straight forward, I.e. They'll fit together

The places to look for tight or loose tolerances is at the following places:

1) barrel nut - should be torqued to no less than 35 ft/lbs with a nice snug fit when you slide the barrel into the upper receiver - if it's loose you'll want to note that

2) handguard to barrel nut to receiver - line these up straight and get the handguard as close as possible to the front of the upper receiver to minimize gaps. If your gas block is perfectly aligned to the barrel you can use the gas block as an index for centering the handguard

3) charging handle - some run the top of the buffer tube , it shouldn't rub at all so if it does try a different charging handle, this is when the upper and lower are joined.

4) takedown and pivot pins, should be snug but not to where you need to beat them to move them

5) lastly hand cycling the bolt carrier with the charging handle should be butter smooth, no binding or hang ups - you may have to oil it well and hand cycle 50 times to get the parts to break in.

Have fun and shoot straight