Corded Drill--Every homeowner should have a corded 3/8" drill and an extension cord. If you have electricity, they work.
When my boys got their own apartments I gave them a very basic set of tools including a corded drill and a small set of drill bits. Since they were unlikely to need a drill often or for any huge jobs, I wasn't going to spend $100 for a decent cordless drill and the batteries that come with cheapie cordless drills wouldn't be usable if uncharged and unused for many months(years) at a time.
I have cordless and I like cordless but I know I can always count on my corded drill to be ready in a moment's notice for light or extended duty.
I recommend a USA made older variable speed reversing B&D, Craftsman, Skil, Makita (USA or Japan), Milwaukee, DeWalt, purchased used for under $20 (perhaps much under $20). I happen to not mind chucks with keys but that's up to you.