what I'm not understanding is if there is any compatability issues. I've heard things here and there. Is it a matter, mostly, of just pinning the two together and spitting some lead or what? No headspace or feed issues to look for when mating two entirely different brands?
Also, when one says MILSPEC are they referring only to the diameter of the buffer tube?
When they say milspec for a lower, they're meaning things like pins being properly sized and in the right location, the magwell being properly sized, etc. There's no such thing as a truly milspec lower for our use; those have the sear pin hole, and we can't have those. So the next best thing is just a quality lower that's otherwise to spec, and there's very, VERY few that are not.
As for headspacing and feed issues, nope, no issue. Headspacing is more an issue of the barrel and barrel extension- there's not one thing you can do about that. Sometimes you can get tolerances stacking between that and the bolt, but I've never had an issue with it and it's extremely rare to hear of one.
Feed issues are usually mag related in an AR-15. Don't buy crappy mags and you usually won't have a problem.
No, you don't have to worry about mixing brands. So long as the stuff is to spec (again, pin holes in the right spots, etc.), it's all mix and match. For a first timer, you'll probably be using a complete upper, and that's the trickiest part anyway (getting the barrel nut torqued up properly), so you won't have any worries. If you're just throwing a LPK into a stripped lower and adding a stock kit, just make sure you get the hammer spring done properly and match the stock to the buffer tube*, and you won't have any issues.
* Commerical vs. milspec buffer tubes (aka receiver extensions) are more a matter of outside diameter than an issue of actual quality. Commercial tubes are slightly larger in diameter with threads cut in; milspec tubes are smaller O.D. with rolled threads (quick way to tell them apart: a milspec tube's threads will stick up over the surface of the tube, but the commercial tube's threads don't). Theoretically the milspec threads make for a better mate into the lower, but in practice that's not a real issue unless you use the rifle butt as a sledgehammer. There's no difference in the buffer itself and a spring. You just have to make sure you get the right stock for the tube; a milspec stock will jam on the commercial tube and not move while a commercial stock will be very loose on a milspec tube. There's more stock options available for a milspec tube, but if you find the stock you want in the appropriate tube, it doesn't matter which you have.
AR15, some assembly required. Inserting a pivot pin and a take down pin is not assembling a thing! I'm surprised at how many ways the hammer spring can be installed incorrectly.