Probably G D & A are the most popular but C , F and the flat keys do sometimes crop up. The late Jim MacLoed used F quite a lot. Some bands use the 2nd box to play mainly chords on both ends rather than the melody which is the province of the first box and the fiddle.. Jimmy Shands winning formula was himself and the filer playing the melody and 2nd box,piano, drims and bass playing the dunt or rhythm.
As to popular dances I would suggest - dashing white sergeant, gay gordons - Canadian barn dance, eightsome reel, St bernards waltz, waltz country dance,strip the willow, Virginia reel,etc etc. The actual tunes played for any of these will vary from band to band and the most common way is to use 3 x32 bar tunes, repeating the first tune at the end as a 4th tune to provide a total of 128 bars per dance.
There is a very useful set of 4 books with loads of tunes with suitability for a particular dance or type of dancebeing stated
They are the first ceilidh Collection (and 2nd 3rd and 4th) published http://www.bel.net
george