Nicole, I don't see where you are. This has a huge impact on what kinds of sushi you will try. Not all sushi has nori (seaweed) in it -- some is little rectangles of rice with a piece of ... something ... on top. Because we live in a small midwestern town, when we had our sushi party we purposefully had no raw fish, 'though I love it dearly, I'll only eat in in towns that have daily flights from one of the coasts (yes, I'll eat raw fish in Chicago or even Madison or the QC, but it isn't a good idea here). A perfect example of sushi is a bit of omlette on a rectangle of rice --- no fish at all, no seaweed at all.
Hubby and I have introduced many to sushi, and almost all who like food at all have loved it. Raw ahi (yellowfin tuna) is a very clean, fresh, crisp flavor. I thought I'd hate eel, but didn't realize that it is usually smoked and really does (as previously mentioned) sort of taste like barbecue served on rice. California rolls were invented to introduced novices to sushi, and are my secret vice. I know it brands me, but I still love them best.
When I moved to Hawaii (in my late 20s) I didn't like fish at all, period. Then I realized what seafood can be. My introduction wasn't sushi at all, but ahi sashimi (sashimi IS raw fish). I was very hesitant, and was amazed that ahi sashimi tasted much like the best raw beef (I've always loved steak tartare and carpacio) -- crisp, clean, fresh. I found sashimi easier to start with than sushi!
Never, ever let anyone tell you that you won't like something. You're a grown up. YOU decide what you will like. Start with California roll (the nori is inside), and go with a maximum of 4 people, and sit AT the sushi bar. Just watching these great artists at work is half the fun.