Congrats on the new boat. I've learned not to use anything too harsh on the vinyl- chlorine weakens stitching. On my current boat I've been using the boat soap I use for decks, and once in awhile I use some marine upholstery cleaner. Thinking lately that an automotive upholstery cleaner is probably just as good and cheaper, too. When I run out I'll buy some of that. I use a Mr. Clean Magic Eraser for spot cleaning, then flush it well with fresh water.
Boat covers shrink over time. For the really tough snaps you can buy snap extenders like this..
On the really bad stains, we have used the magic erasers. simple green for the rest. What will help you with the covers, is get them in the hot sun first. then install them and try to leave them on. Works for us. Dave-R