So if I haven't watched Twin Peaks before, is it wise to go in all fresh or should I watch the original first?
Definitely watch the original first, since the new season is a direct continuation of the plot of the original but 25 years later.
How do I watch the new stuff without getting a subscription to something I won't use otherwise? I have a Netflix account, but it's not on there.
Check the twin peaks subreddit, there's a list with how to watch it depending in your country. Maybe you can get a free trial in some services. Or if you already have Netflix, you can use a VPN that sets your computer as if it was in Latin America and watch it there, we have the four parts with original audio and also English subs.