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You're getting different answers because lots of people do it a little differently, and for the most part, they all are successful. There is no one single "correct" way.

The most important part is keeping the seed moist. If it dries out during germination, the whole thing's over. Both the methods you mentioned should work. If you go with a damp towel or paper towel, I might recommend putting it in a plastic bag to prevent fast drying out. Moisture is the key. The medium is less important.

A satsuma (cherry) seed also needs to be cold stratified. Cherry trees grow where there is winter. So the seeds have a survival feature - they wait until they've sat dormant through a winter, then they break dormancy. This keeps them from germinating in late summer or early fall, and then not doing so well the first winter because they're so tiny.

Go ahead and try germinating your seed. If it sprouts, everything's fine. if it doesn't, you can always cold-stratify it in your refrigerator for about 10 weeks, and then try again.

I suggest you go to a store and but a 3 or 4 year old plant. It will take forever for any seeded tree to produce. I grow the tangerines, lemons, and key limes.