I have an early 17 fret Paramount Style A which has suffered much abuse. It is good as a player, but has little market value. I've owned this banjo for decades. I am considering to set it up for Irish tuning and would appreciate some advice about string gauge selection, etc.
String gauges, in my opinion, are largely a matter of personal preference. There are several "Irish" sets available in slightly different sizes from different companies, and you may need to experiment to find the ones you like best.
Because Irish strings are heavier gauge than standard tenor sets (due to the lower tuning, they are heavier to keep string tension about the same) it will very likely be necessary to widen the nut slots and bridge slots in order to accept those thicker strings.
You will need to go for medium or heavy Irish banjo strings for GDAE. The G string can be a bit floppy on a 17 fret hence. You might get more of a response in the 4string Irish section. Most of us use different tuning here (I use cgda).
It's not always true that heavier strings will work better on a 17 fret instrument. Generally, the heavier the gauge, the stiffer the string, which can eliminate floppiness, but the stiffness can also cause the tone and sometimes even the intonation to suffer. The fourth string is usually the worst of the bunch. Again, you should experiment. I actually use a classical guitar fifth string for the "C" on my 17 fret tenor (CGDA tuning) because the usual tenor banjo gauges (about .030-.032) were way too stiff and never had proper intonation when fretted.
You should also, as Carrie suggests, consult the four string Irish section.