I don't know what kind of experience your friend has, how much he will be practicing, and so on, but I think you're on the right track. I would opt for the 25-06. While the .243 will certainly do the job, if it would be a marginal caliber for your friend, I would overgun rather than undergun. Both should be pretty available over the counter.
Unless your friend is a very good shot and really picky about bullet placement (and disciplined enough to pass on marginal shots), I'd probably go bigger than 22-250. My personal thoughts.