IMO, keep it consistent. Make it first 3 letters (or 4) of the location, or the team, but not combinations, makes it easier for the casual fan/those new to twtitter to follow. Not 3 letters of town then 4 letters of mascot or a mix of the two. Set it on one thing.
otherwise:
Brisbane Broncos: Bris
Canterbury Bankstown Bulldogs: Bull
Canberra Raiders: Canb
Cronulla-Sutherland Sharks: Cron
Gold Coast Titans: GCT
Manly-Warringah Sea Eagles: Man
Melbourne Storm: Melb
Newcastle Knights: New
New Zealand Warriors: nzw
North Queensland Cowboys: NQC
Parramatta Eels: Eel
Penrith Panthers: Pen
St George Illawarra Dragons: StGI
South Sydney Rabbitohs: lol@50uff$
Sydney Roosters: Syd
West Tigers: Tigs