In reply to demdyke:
An excellent choice.
Most has been covered already. Sorry, but I can't predict the weather. I'd avoid Feb but any of the other months could be fine, or dreadful! September used to be one of my preferred months, but the midges seem to last longer now so maybe only later in the month. October is often windy in my experience, but it really is pure luck.
The Paps is an excellent longish day out. Don't underestimate how rough going it can be on Jura. Lots of tussocky grass and bog on the lower ground, and as mentioned rough quartzite, scree etc on the hills.
Whilst you're there, you must do some walking on the west coast, particularly the northwest sections around Glengarrisdale where there is an excellent bothy. There are some superb caves to sleep in too, well above the sea as they're on ancient raised beaches.