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.
In Illustrator, you can design patterns, complex graphics and work with type. You can learn to design printables fast with the Basic Printable Design Course from Printable Crush. Illustrator is a highly in-depth program, so taking a course is a quick way to learn the basics.