Never use your local markets seafood case. You need Sushi grade seafood to make your meal. You should find a specialty seafood store preferably an oriental one that handles sushi fish.
Also another tip. Never use freshwater fish in Sushi. Tapeworm eggs lurk in freshwater fish flesh and only high heat cooking can kill them.
I agree with the last poster about using raw fish at your local supermarket. I've seen people rushed to the ER because they used raw salmon at their local supermarket as sashimi/sushi. You NEED sushi-grade seafood. If you're really keen on making your own sushi at home and there is no sushi/seafood market in your area, I would recommend you go to your local Japanese restaurant and get sashimi. Then bring the sashimi home and to make your own sushi. It'll be expensive this way, but at least the fish is safe.
You'll have to see what you can get at your local supermarket. They usually sell some raw fish in the meat section, but it's unlikely that you will find eel there.
I make sushi at home. It is quite an adventure. Sometimes it looks good. Sometimes it just will not roll right for me but it still tastes good.
Use cooked shrimp or tempura shrimp. Use imitation crab leg. Use
lox (smoked salmon). Change the additional ingrediants around. Avacado, cucumber, sesame seeds, cream cheese. Make vegtable sushi.
do you have a Wal-Mart near you? if so, they sell the sushi wraps (seaweed) and the mats. also they have a fish market in the super walmarts. if you can't find any good fresh seafood, you can use vegetables also, pickled cucumber is good, and also anchovy. the best fish to use is blue tuna. you can also use the blue tuna to make sushi-mi (the plain raw fish eaten with wasabi sauce)