What's some safe advice for a beginner for making sushi? I suddenly felt like making sushi. I thought about going to the fish market and buying so tuna and salmon.

Then I figured out that I have to kill the bacteria first. So far, I know that you have to freeze the fish under 20 Celsius.

Is there anything else I have to put into account?
Buy sushi grade fish and it will (well should) have been frozen.  This is in the US.