The advice frequently given is to choose something that doesn't have to age too long so that you can get a few cycles in (that is, so you don't have to wait 3+ months to figure out if you did a good job). A lot depends on what you like.
Caerphilly, a cheddared, hard cheese, is good at 3 weeks.
Those who like white-mold ripened cheeses would tell you to go for camembert which is (at least, can be...) good in about 3 weeks as well.
Washed curd cheeses are tolerant of mistakes. Monterey jack is a washed curd (at least in some recipes...) that is good in about 4 weeks.
I'm sure there are other short aging cheeses that represent other styles of cheese, but those are the ones that come to mind.