I'm kinda in the minority here, but I actually PREFER the 2-1/4" ones.
I had a 3", and they feel OK; but I have alot better control with a 2-1/4" one.
I recently lucked into an ebay auction for a 2-1/4 translucent brand new for $49.99.
I was planning to pick one up from Happ before that auction came up.
As far as the 2-1/4 being "arcade authentic" it depends alot on which game you are playing, and the type of cabinet you are playing it on.
I don't think Missle Command is truly authentic on an upright cabinet without the 4-1/2 ball that was on the dedicated uprights.
The 2-1/4 is authentic for it on a cocktail though, as I think the cocktails shipped with 2-1/4 balls on them.
Marble Madness and Crystal Castles have to have the 3" translucents.
Those balls are what made the games IMO.
I've played Crystal Castles with a 3" white replacement on it, and it's just not the same without that glowing red ball.
Centipede usually had 3" balls IIRC, but Millipedes shipped with a 2-1/4 on them, so either could have either size and be considered authentic IMO.
My personal preference on trackballs is that I like the 2-1/4" for precision work (Centipede/Crystal Castles/Missle Command) and 3" for games like Golf/Bowling/etc... where you pretty much just need to spin it in one direction at a time.
As far as hooking one up without an opti-pac, the best option I've found is Oscar's USB mouse hack.
It's pretty inexpensive, and works really well.
I've rigged a quick disconnect on mine to let me swap out my spinners and trackball on it, with great success.