Some thoughts, but not an exhaustive list.

You'd likely do best to have your real estate agent guide you. If he or she is not an expert on wells and septic systems assign him to get you some expertise that can help.

1) Flow rate of the well. Does it support the current closets.
2) Well pump and reservoir.
3) Water quality from the well - all the tests, get a current test, especially testing for bacteria and contaminents.
4) Has the well ever frozen or stopped providing water? Any pools or hot tubs that need to be fed by the well (that require large amounts of water)?
5) What's the septic system certified for? Does that support the closets in the house? Does it support adding any closets?
6) What's the leach field? Notice any issues around the leach field? Does it pass under a driveway that could compromise the driveway?
7) What's the septic pumping requirement? I could get away with getting mine pumped every Presidential Election year. Will your family be large and require more frequent pumping? What was the cost of the last pumping or two?
8) What are the materials between the house and the septic tank? Is it clay that roots can grow into joints and clog it?

I know there are PLENTY of other considerations. You should get a pro with a full-blown check list to guide you through all the considerations.

Neither is a big deal in general. Having a well is fine, having a septic tank is fine. However, things are different from city water, so don't paint yourself into a corner by not performing the due diligence up front. Best of luck.