Costco has some good frozen fish options- Sam's does as well, but not as good as Costco. I would stay away from tilapia as it's not particularly healthy as far as fish goes. Of course if you can tolerate salmon, it's the best choice both from a health and taste perspective IMO. Wild caught only (not "Atlantic" salmon, which is farm-raised).
I like to poach salmon. half water, half white wine in a pan. Some garlic or shallots in there. 5-8 minutes simmer, covered, and boom, perfect fish, no smell.
Go to a nice seafood place in Kemah or something that has fresh fish. That will give you a good experience and encourage you to try it again.
I enjoy the much cheaper imitation kind: I cant believe its not real puffer. I cant even tell a difference.
I recommend tuna as a light fish-tasting fish that's pretty healthy and easy to find. Butterfish is a great-tasting fish with little fish taste, but it may be hard to find or expensive.
If you can get a fresh redfish fillet, cooked just about anyway you like, nothing beats it, in my opinion (and not "fishy"). Be careful with the sauces that some places like Pappa's charge extra to put on top. They're delicious, but if shellfish might give you allergy problems, ask whether that's in it. Sadly, redfish has gotten ridiculously expensive these days. We spent a couple of weeks on Isla Mujeres a while back and I had it fresh nearly everyday. A nice redfish filet caught that morning with all the trimmings was around $7 at one of the local family run places. Heaven!
Fish are all so different so it's going to be hard to judge based on the first few you try. Do you live in Houston? If so Rockfish on Westheimet or 1960 is a good place to start. Their Pecan Crusted Trout and Cedar Plank Salmon are great and won't break the bank. Redfish, Tilapia and Flounder are good and if you want steaky try Halibut or Swordfish.
You must go to Papadeaux at once! Start with the spinach artichoke dip with lump crab, served with garlic bread. Shellfish allergy be damned. Follow it up with the Texas Redfish Pontchartrain. Wash it all down with a Grand Hennessy cocktail. Thank me later and after your trip to the ER/Urgent Care. Trust me, it'll be worth it.
This is a good idea for someone not used to eating seafood. If you are in Houston, there are great places to eat along the coast that would provide a good first experience. Some of the less fishy fish that are caught in Galveston are speckled trout, redfish, and flounder. Some places cook with Cajun flavors or fry it, which can also help with the taste.
This is probably the way I'm going to do it. If I'm going to dive in, it should at least be something good. If not that, I'll coat it in Tony Cachere's.
Topwater Grill in San Leon Down to earth, great view, as fresh as it can get http://www.yelp.com/biz/topwater-grill-san-leon
