"Sushi" is rice seasoned with vinegar and other ingredients and served in a number of ways, with all sorts of toppings and/or fillings: sliced rolls (maki), handrolls, or individual pieces (nigiri), to name a few. Not only is there a wide variety of cooked seafood choices, you can be a vegetarian and still pig out. Don't just try the usual California rolls!
Futomaki is a large roll that contains a number of ingredients (usually tamago, a sweet egg "omelet"; pickled radish, mushrooms, and/or other vegetables). It is a great "starter" sushi. Other good choices are ebi (cooked shrimp; not "ama ebi' which is raw), unagi (cooked freshwater eel with a sweet glaze...eel is just a long fish, so don't freak out), king crab nigiri (a piece of cooked crab leg on rice), and "spider maki" (deep-fried softshell crab inside a rice roll). Tako (octopus) is not raw, it has been boiled but it needs to be prepared properly or it will be tough.
If you want to test the raw waters, start with tuna. Good raw tuna is far more mild tasting than cooked tuna. It isn't "fishy" at all...and if it is, then you want to high-tail out of that particular restaurant! Raw scallops are also really sweet and mild if they are fresh.
I went to Japanese restaurants for years as a child in SoCal and never dared try raw fish until I was 18 or 19. Then I went for it and have been hopelessly addicted for 30 years. Just go for it! I don't understand why so many people are afraid of something as pristine and simple as perfectly fresh fish, yet think nothing about chowing down on "factory food" that contains appalling ingredients. Of course, there is some risk with raw seafood, which is why I say "there is good sushi and there is cheap sushi, but there's not much good cheap sushi." Be adventurous!!