For most of my work I play on a 1949 Conn 6H. I love playing it, and it makes me feel connected to the great tradition of jazz trombonists.
I also play a newer Conn 88H – it served me very well in college, although I no longer have occasion to use it very frequently.
I play Doug Elliott mouthpieces, which I think are the greatest mouthpieces in the world. I use an XT LN104C2 on the 6H and an XT LN104G8 on the 88H.