Hi there Jennie
First off, good luck with the graft if that's what you finally opt for. It's never an easy decision. But I think you know when you're ready. Then of course, you get all the questions popping into your head !
As for the medication, the typical course is as follows (this is a "standard" approach -- of course, there's no such thing, but this is what you tend to start off with -- it can be that the medication(s) get tweaked depending on how things go after the graft).
1) An antibiotic drop (Chloramphenicol is the norm) -- between two and four times a day with a higher dosage initially which is then tapered off after the first few weeks. This is to prevent infections.
2) An immunosuppressant (Dexamethasone would be the default choice) -- often four drops a day to start with, reduced after a few weeks. This is to prevent rejection.
That's it !
The problem is, if things don't go by the book then all bets are off. If you get a suspected bacterial infection and it doesn't respond to the antibiotic you begin with, you'll get prescribed alternatives which are more effective. If you get high intra (or is it inter ? I can never remember !) ocular pressure you might get a different immunosuppressant steroid. Or you might get different drugs to lower the pressure. If you get a viral infection then you'll get Acyclovir (probably orally). And so on.
What my experience taught me is, don't dwell on it if you can (ha ha ! the easiest thing to say, not at all easy to do in practice I know). While complications can and do happen post graft, I don't think we've ever had anyone post here who ended up with a catastrophic sequence of events. Some people have had a lot worse a time of it than others, as you'd expect. But I think everyone has -- eventually -- come out the other side. That uncertainty is what makes it such a hard thing to mentally prepare for. You hope for the best, but you have to be prepared for the not-so best too. Like I mentioned, that isn't simple. Take my graft for instance. I got a HSV infection which was the last thing I expected or wanted. I then kicked myself for not advising the consultant that I get cold sores very frequently when a mucus membrane is compromised (e.g. a shaving cut or badly chapped lips) -- so it wasn't that surprising that I got an ocular HSV blister, even though I'd never had it happen before, considering what the procedure entails. It was a terrible feeling of helplessness and worry. But good quality aftercare and a course of Acyclovir sorted things out so I needed have been concerned. An experienced surgeon will have encountered situations like that before and will know how to handle them.
Hope I've helped, have a bad feeling I've probably caused you worry

-- I do hope not though. Just trying to say not to fret about having a graft without being too Pollyanna-ish and underplay the significance of what is after all major surgery.
Best wishes
Chris