my must have tools are a nice set of roll pin punches, a brass or nylon hammer, needle nose pliers, correct hex keys (for the trigger guard), and the castle nut wrench.
automatic center punch helps in staking the castle nut (they come loose) and a thin, sharp knife helps to hold the front detent and spring down while you insert the takedown pin (a slave punch in the right diameter helps).
everything else is just "nice to have" and can help speed up the process. a vise, a lower block, roll pin starter punches, the specialized ar-15 wrench (armorers tool), slave punches, vise grips all fall into this category. if you're gonna assemble an upper too, you'll need some of these. I've done probably ten uppers and lowers.
my first lower took about an hour and a half. the last one I did took less than 20 minutes.
some things to consider...some lpks such as the cmmg kit are color coded and have a diagram to keep your pins, springs, and detents straight. some of the parts are easily confused.
also, if the hammer is easily held in place while you insert the pin, the spring is probably not oriented correctly. it needs tension to ensure adequate force when it strikes the firing pin. you're gonna have to fight that tension while aligning the pin.
there are some excellent resources that know much more than me about ar-15 assembly in this thread. if you get stuck, just ask.
good luck!