Get a 24/2.8
An AI or AI-s is what you need. These lenses will couple to the last version of the F2, as well as the earlier ones.
Here is a link to the Nikon sight, showing the latest version:
AI-s, under $ 200 US. AI, less. AF, $200
"One of the painful things about our time is that those who feel certainty are stupid,
and those with any imagination and understanding are filled with doubt and indecision"
Since the camera is a F2, why not a non-Ai for that? I used to have a non-Ai 24mm lens years ago, and I liked it a lot. All of my lenses were non-Ai at that time because I was satisfied with their quality and didn't feel like paying extra.
As long as you pick up a Nikkor lens, you and your friend won't be unhappy about the results that it produces.
As mgb stated, the model of F2 determines the lens that fully functions with the F2 metering system--if it has one. There was an F2 (without meter), F2 Photomic (which requires an indexing prong on the lens), F2A (which uses AI lenses--"auto indexing"--which still have the prong). I might be mistaken but later lenses will all fit the F2 but they don't have the prong for indexing. I used Nikons from the early 70's through the 1990's but I never owned one newer than the F2A.
Incidentally, the 24/2.8 is a killer lens.
Yes, the D lenses will mount on the F2. I believe that if you have the older prism the meter (with the indexing prong) the meter won't work.