For that job, white PVA, AKA Elmers, will do just fine. The yellow PVA like Titebond are a little too thick for veneers, they are made for joinery. Traditionally, hide glue is used but totally unnecessary, and stinky, unless you are faithfully restoring an antique piece of furniture.
Resorcinol glue, is a good choice for veneer or wood joints that might be in a damp-wet environment.
You can make Iron-on Veneer, by coating both surfaces with white glue and allowing them to dry throughly then use a cloths iron to press the pieces together. The glue must be applied evenly, a small paint roller works well.
Edit, Cross post! Firstram, has a more detailed explanation above.