I'm making a small jewellery box at the moment to house my wife's Xmas present, a pair of antique art deco earrings that a cardboard box just doesn't do justice to!
Anyway, it's only about 2" square and I'm using maple veneer on the lid, glued on to a piece of Boxwood. You don't need a press for small stuff like this, I just glued it with PVA and sandwiched it overnight between two scraps of 18mm melamine faced MDF with a G-clamp, the glue doesn't stick to the melamine.
Have to say I don't like pre-glued veneer, it can creep, and the heat applied to the veneer can make it shrink and split, I prefer to use cold glue and take my time.
I buy veneer from many sources, mostly though I use Vale Veneers who have an online shop and also sell on eBay.