very simple. you print 2/3rds of the print, so that you can insert the allen key so that it's flat to the surface of the print. then print the rest.
either pausing the print, or doing it in two seperate prints. starting the second at the exact height the first one finishes.
I presume the handle end of the allen key has the standard right angle bend ?

As far as what printer - what's your budget.
bear in mind that once you have a 3d printer you will find hundreds of uses for it.
So don't limit your budget by thinking it would be just for this one job - it absolutely would not be :-)