sounds like fun! here are some thoughts:
1) hiking boots with gaiters are fine! if the boots are not low cut you probably won't even need gaiters. i see people do it in lesser shoes pretty often ...
2) crampons are not generally needed up to muir. i don't think i've ever worn them and can't really remember seeing anybody else either.
3) no self-arrest should be needed up to muir if you stay on the main trail. it's not that steep. if you fell and slipped you'd eventually stop. some people slide (glissade) on purpose. you can find "steeper" sections if you want to practice self-arrest, though.
4) the biggest risk will be navigation in a whiteout. plan accordingly. also drink lots of water to avoid dehydration, and bring warm clothing and sleeping bags. (it can be a hot 90 degrees at paradise and chilly and blowing 50 mph winds at camp muir.)
have a great time!!!