So in my experience (which isn’t extensive with outdoor in my 25+ year WWing history), always glue wood to wood unfinished and yes, Titebond 2 or 3 should be fine, although recently Ive been building a Teardrop Trailer and it’s been outside for about 4 months now and some of the finish pieces are pulling up - I used Titebond 2 to hold those down, so something different that’s listed as outdoor waterproof might be better. I dunno. Most everything I’ve ever done for an outside project has always had fasteners of some kind - pin nails, screws, etc. If it’s just a 1/8 inch to 1/4 inch thick letter, that would be overkill. Glue should work.
As far as finish is concerned, if you’re sticking with a natural look - Spar Urethane is what you want. Polyurethane can work, but it’s not meant to take the UV. Spar is specific to outdoor / marine environments. Keep in mind you’ll need about 6-8 coats to really make it effective. I have 4 on my tear drop trailer and it’s not enough. You also might want to run a very very thin bead of silicone around the letters after you are finished with your last coat. Water will pool / get into any microscopic crack in anything, so having a good outdoor silicone will help quite a bit. It’ll take a while and you want a really really small bead so it’s not noticeable, but it’ll be worth it.