What you can ask about as you continue to communicate with faculty in making your decision are things you can apply for later like fellowships, grant opportunities for research, extra teaching (e.g. summer school or sometimes you can get extra for proposing and teaching a class of your own design), funding for research/training-related travel, summer programs, etc. related to your goals and interests. These are things that the school or department may offer or will support your application for later. You’re more likely to be among the first to hear about such opportunities and be nominated for them if they know you’re interested up front. More importantly, it shows you’re prepared to take advantage of every academic opportunity you can, a good thing, rather than committing a potential faux pas and coming across as arrogant or “entitled” (even if you’re not). Having a strong application is only the first step–if you start off on the wrong foot on a personal level, it’s not going to be a good year for you.