The least radical option is to work on straight-haired acceptance (could save you plenty of time and money). But that's my bias. That said ...
There are methods for curling straight hair, but none of them are spectacular for the "health" of your hair, and it can all be time consuming.
Perms generally dry out the hair and often look fake and/or stringy. Also, re-applications are a chore, and costly. Curling irons=potential heat damage. Even air-dried roller sets can cause problems because of the tension they create. You could try an overnight flexirod set. I'm sure there are other options.
You might get away with doing most of the things listed above if you do them in moderation. Some of us curlies straighten once in a while and are fine with it.