What billing cycles can I pick from, and does the length actually change the price?

You've got monthly, quarterly, half-yearly, yearly, and the lifetime one-time option. And yes, the cycle changes the effective price noticeably — yearly works out to roughly half the cost per month compared to paying monthly, with quarterly and half-yearly landing in between. It's the classic subscribe-for-longer-and-pay-less model. If you're confident you'll keep using it, the yearly (or lifetime) option is the sensible money move; if you're still testing the waters, monthly costs a bit more but keeps you flexible.