All this really depends on the fiddle.  Strings can sound quite different on different instruments, but medium would seem to be a sensible start; you can always try variations next time.  I've used Dominants from time to time, but I can't remember which type (I tend to prefer narrower, all-metal strings, and have had good results from Pirastros with a Dominant E as spare).  The same goes for tuning; some instruments will take a new string quickly and maintain pitch fairly well straight away, others prefer you to work up to pitch gradually.  If you haven't been playing long, and if the fiddle hasn't been played much either, then I should take it slowly to begin with; change -and retune- one string at a time so that you don't risk moving the bridge or soundpost out of line; keeping the tension on the instrument even is always a good plan.  Don't forget to stretch the strings manually a little from time to time as you raise the pitch; this will help.

Malcolm