This topic was dealt with recently. Try clicking on the following link.

http://www.boards.ie/vbulletin/showthread.php?p=54342474#post54342474

But very briefly, the things that might affect your application are,

Your Firearms Officer / Supers attitude towards firearms.
Calibre will always raise eyebrows.
The "idontlikethelookofthat" excuse.
Club membership is a must.
Security & safe-storage at home.
Your own back ground, the list goes on and on

But, if you have a reasonible need for having that particular firearm and providing your back ground is good, there shouldn't be a problem.

Largest calibre allowed........again, it depends on your need for it and possibly all of the above.

I beleive that the Midlands are authorised to allow the use of all firearms that are Licenced / Certified by the Garda Siochana to shoot on their range, that could be anything from a .17 up to gods knows what.

More than likely you will have a lot of responce to your queiry......best of luck.