Barbecue on wood fire
The best BBQ's are wood fired, you get real wood smoke flavour. Anything else is just a just outside hotplate/grill, and might as well be electric

Using charcoal is easy and safe. A simple hack is to use some small pieces of strong smoke flavour generating wood on top of your charcoal when you are actually cooking

Smoke is all part of the BBQ experience, and after a little practice at fire lighting techniques, shouldn't become a big issue. Join the local Scout group as  leader, and they will teach you how to make good cooking fires :-)