Not always the cheapest gift (the cost entirely depends on the studio fee at your local paint-your-own-pottery shop), but a fabulous & personal creation is the hand-painted coasters. (The tiles are generally one of the cheaper items to paint.) Here’s a set I did as a wedding gift.
After a bit of scribbling on the back and tracing over my lines, I was good to go. Graphite burns off in the ovens, so pencil tracing your design is a good plan if you’re uncertain about your freestylin’ skillz. ;-)
Another simple way to go is to use a foam stamp (it also takes much less time). Most pottery shops have their own, but you can pick some up pretty cheaply at any craft store. With a stamp you’ll still need to go back over the design with a paintbrush, so the simpler, the better. (I usually take my own cheap brushes too; hundreds of little hands make for some gnarly brushes.)
Had I remembered to run by the pottery store yesterday, I’d have a newly glazed set to share, but that will have to wait until next week now.