Hi
I too have a Union Graduate lathe and the chuck thread size you're after is inch and a half by six tpi. If you have the lathe with two threads (one of each side of the head stock) then you can get a chuck which is left and right hand direct thread. Robert Sorby make these. Thats the chuck I use and I personally can't fault it.
For spindle work you need a 3MT drive centre and a 2MT live centre.
Hope that helps. If you have any more questions about your lathe then please PM me, I'll be glad to help if I can!
The Union Graduate is a superb lathe, by the way. You won't regret buying one.