I have never fished in Alaska for the big rainbows there, but from what I have read and my experience with trout of all sizes here in Virginia I would say a 7wt 9'-0" rod is great advice for Alaska trout and the bass of your rivers and lakes.
I have rods from 3wt to 11wt and the 7wt (I have two) get as much use as any I have. Throwing big streamers to trout, bass bugs to Large and Smallmouth Bass, plus red fishing and speck trout on the coast is what a 7wt is made for. I love mine.
TFO makes good rods for the money, I just bought some for my grand kids. For a reel Ross or Lamson make mid price reels that would give you good service and be somewhat salt water resistant. You mention the Gulf coast and a reel that is salt safe is a good idea, but they all will need a good cleaning after using in salt.
Fly line is as important as the rod so purchase a good one.
I agree with those who suggested casting lessons. A good instructor will have you
casting good enough to fish in just a few hours of instruction, plus a few days on the water and you will look as though you have been fly casting for years.
Any good fly shop can get you connected with the right gear and a good instructor.
Welcome to the fly fishing community!
