There is a particular pleasure in giving something that was made slowly. A handmade mug or bowl says, without saying it, that you spent more than a passing thought on the person receiving it.
Start with a mug. It is the most used object in most households, and a good one becomes the cup someone reaches for every single morning. A pair of tumblers makes a thoughtful gift for a new home, and a single statement bowl can anchor a whole table.
For someone harder to read, a small catch-all dish is almost universally welcome — keys, rings, coins, the small things that go missing. And if you want to give an experience rather than an object, a place in a studio class is a gift that keeps unfolding long after it is opened.
Whatever you choose, wrap it simply. The object should do the talking.