Shoku in Grandview is good. I get from there often.
Kooma near the Short North (across from the North Market) is great. I eat there almost once a week.
Haiku on High Street in the Short North typically gets mediocre reviews, but I love it. They're shrimp tempura roll is how I got hooked on sushi, and now it's my favorite food. They have some great regular entrees, too. The General Tso's and Mango Chicken are both fantastic.
I have heard great things about Typhoon in the Arena District/Short North, Otani (I believe it's north side), and mediocre things about the sushi "conveyor" bar (do not know the real name) on High Street across from the Convention Center. I have not yet tried any of these yet so I cannot tell you for sure.
I can tell you where to NOT get sushi. Do not get it from the grocery store, Lemongrass on High Street, or from Nida's in the North Market. If you go to any of these first, you will probably never eat sushi again. Even a sushi fanatic like me can only stomach one of these places every once in a while, in a pinch.
As for starting out, start with the fried rolls. Tempura shrimp, Kooma has an awesome "Resource Roll" which is fried under the rice. These cooked or mostly cooked rolls will get you hooked. Then move into the milder raw stuff; yellowtail, tuna, salmon, and crab (crab is usually cooked) will get you started. If you like spicy things, try their spicy variants and it will make their introduction that much better. Then you can move into more intimidating things like eel (cooked and when done correctly, awesome, I recommend Kooma for eel), octopus, and mackerel. All good tastes. Then move into nigiri (raw with a little spot of rice) and sashimi (raw, no rice). Skip the California Rolls, they're for kids and a waste of money if you're looking to be into sushi.
Good luck.