Best athlete (among homegrown star players) is probably Walter Jones or Shawn Kemp.
Biggest superstar is probably Griffey, though I could make a case for several other Mariners.
The best player to ever play for a Seattle team* was Randy Johnson, IMO. Johnson is statistically the the best LH starter in MLB history, and we had him for a decade. To put things in perspective, Felix Hernandez's numbers are a full step below Johnson's and Felix is maybe the best pitcher in baseball right now. And Felix is pitching in a bit of a mini-deadball era where offense is way, way down. Johnson played during the steroids era where homeruns were being hit at a rate never seen before. It's just crazy to think about how good Johnson was. It might be another 100 years until we see another like him. Oh, he also threw 100 MPH when he was almost 40 years old. During his final years he still had a fastball that (literally) vaporized a pigeon. I don't know why he isn't remembered as a Seattle icon more- probably because of how he left or perhaps because he looked like a posterboy for faces of meth.
I guess you could argue that Griffey was the greatest LH position player (that stayed clean), too. It's kind of amazing the kind of star power the do nothing Mariners have had, isn't it?
Then again, you could make a case in a few years that Russell Wilson could top both those lists. Wilson is a phenomenal athlete and a legend in the making.
*(excluding Jerry Rice, heh)