I recently bought a vintage adult tricycle but not sure what type of lock is best. Any recommendations?

Where are you locking it, and who are you protecting it from? Professional thieves probably won't be interested unless it's a work bike, and even then the contents are more attractive. Tweakers and scum usually want something they can throw in the back of a van and sell quickly.

Personally, I'd lock the frame to something solid, and if the front wheel has skewers rather than nuts, lock that to the frame. If you're not going to be gone all day, or the bike isn't that valuable, a heavy duty cable and padlock are probably enough. If it is valuable, a ulock or pair of ulocks.

Yea where do you live? is it a place where a lot of bikes and trikes go missing, ? Or would just keeping a wheel from rolling be good enough?

Like the above.. It will bt heavy.. . but ,, 3 Meters of hardened security chain * and a heavy duty Padlock or a Mini U lock from a Quality manufacturer is one approach..

* better than a Cable, but not as Light..

You bike most likely does not have quick release wheels and must weigh over 45 pound. So I would just get a cheap cable lock to secure it to a post or fence. Anyone stealing it will need tools and a strong back.