Welcome to the club!
You've started with a loaded question. If your car was maintained reasonably well, it should last a long time. Your 300SE has the M103 engine which appears in several models and is a workhorse. I've got the same engine in my '88 300SEL. I'm at 143k at the moment.
On the flip side, to quote another member here, "There's nothing more expensive than a cheap Mercedes." This is basically saying that if the car wasn't maintained much, if at all, it will cost a fortune to get it back in good shape.
For the transmission, if you don't have any service records, you should change the transmission fluid and filter before checking anything else.
1988 560SL Black/Palomino
1988 300SEL Black Pearl/Burgandy
1984 500SEC Anthracite Grey/Palomino