You'll need adhesives to assemble certain printables, like attaching cupcake toppers to paper straws. A printable designer's go-to adhesive is usually a hot glue gun. They're inexpensive, and the glue is guaranteed to keep everything in place. You can also use glue dots, double sided tape (permanent is preferred), glue sticks, or regular tape.
The biggest question is whether you should get an inkjet or a laser printer. It depends on your needs. If you plan on printing a lot, the toner in laser printers lasts a long time, but the replacement ink can be pricey. The color on laser printers is much more vibrant than an inkjet. However, inkjet ink is relatively inexpensive but plan on replacing it often. Inkjets also print photos better, so if you use photography in your printables, that is something to consider.