I've never freelanced before, but what I've heard is that it's a lot better to offer up a freebie than a low price, as long as (1) the freebie is small and fixe

I've never freelanced before, but what I've heard is that it's a lot better to offer up a freebie than a low price, as long as (1) the freebie is small and fixed in scope, and it's mutually understood that any substantial support/follow-up work will be paid, and (2) there's a pre-existing relationship with the client, so that it can't be construed as a desperate/promiscuous willingness to do free projects for anyone. The reason a low-priced project is bad is that it's difficult to raise to a decent price without upsetting the client. Whereas for a freebie, there's an expectation that the price can go up. Moreover, low asking prices tend to lead to low-end work.