What are the most important factors when considering graduate school in chemistry?
As a second year grad student in chemistry, I would say the two most important factors are if there are multiple professors you could see yourself working for and if you feel like you could spend the next 5+ years of your life at the school/in the area. You are going to be stressed out with work, so you want to enjoy where you're living.

I haven't heard of any US chemistry PhD grad programs that don't pay tuition + insurance + stipend, so I don't think that's much of a worry (I would, however, make sure you get all that).

The renown of the school and success of past alumni is actually less important than you'd think. Grad school is all about your research advisor and your research (i.e. a better professor at a lower tier school is better than the other way around).