I've been playing mando for close to 40 years, but never took it seriously enough, so maybe I could comment here?
For Celtic I think an oval-hole mando sounds good. A's are cheaper than F's and don't sound different to my ear. (Both my mandos are A's; a teens Gibson oval and a Flatiron A5-Jr with f-holes.) Kentucky has some oval-hole models, both A and F, but I haven't tried them so can't recommend or disrecommend them.
Flat-top mandos have a good sound for Celtic and old-time, and there are several builders out there, e.g. Big Muddy, or Northfield's Calhoun model.
I've liked wider fretboards when I've tried them, but neither of my mandos has one, and it's not really a problem. (At least, not a problem compared to stretching your little finger to get some high notes.)
If you want amplification, that probably means retro-fitting a pickup.
I've met a number of people who were intrigued by the tuning being "the reverse of a guitar", but that never helped me much.
It might be helpful to get yourself a book of fiddle tunes - I like the Fiddler's Fakebook, which has tunes from a variety of styles, including Celtic. (It's in standard notation, but the Mandolin Fakebook has tab.)
D.H.
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