Light! Light colors and as much window as you can.

Also tile on the floor. It is much easier to keep from getting musty and to clean after a problem.

Also be sure the heat works well for the winter and the dehumidification for the summer.

I wished I had put in more closet and shelving space and tile instead of wall to wall.

If you aren't skilled in doing the basement work, leave it to a pro. We passed on several houses recently due to basements that were DIY that we would have to completely "do over." Don't do a wood floor. It's a mess if your sump pump fails. Don't do a dry wall ceiling. Looks great, but --- we've been in the house less than a year and have pushed up ceiling tiles for numerous repairs, home theater speaker runs, ethernet, fire alarm, plumbing problems, etc.

We have finished our basement in our old house and again in our new place.

Most important - lights - we put in 1.5 more high hats in our basement that we did on our first or second floors where we have more natural light.

We put in a half bathroom if we had the room I would have put in a shower stall - a half bathroom is nice when you have company or if you have children their friends are over and they can stay in the basement and leave the adults alone and vice versa.

We also put in a lot of built in storage areas with doors.

We put in carpet and as long as you have good HVAC system you won't have any musty odors.