Z visas are a thing of the past at least in quite a few places now. Nowadays the latest is a sticker in your passport that is proof of both your residency status and your permission to work, and in these places separate "residency permits" are no longer issued thank goodness - they were just another thing that was too easy to misplace.

Sure you don't have an L visa? Anyway, regardless of that, it's standard procedure to undergo a medical check here, so if you can get one at home and can get all the necessary things ticked off, it might save you the money and the few hours hassle of doing it once you're here. Just get the form from the embassy - you'll need to be checked for a range of conditions just mainly to give them a reasonable expectation that you won't drop dead soon after arrival nor will be responsible for starting any epidemics - pretty standard stuff. It might be that the embassy no longer issues these forms because z visas and res permit booklets are going the way of the dodo here now.

Anwyay again, it's nothing to worry about. If you bring your own med check form and they accept it, lucky you. If not you'll probably but not definitely just have to go through the rigmarole when you get here. There's always going to be a easy solution once you're here, so don't fret and just roll with it. Often college officials can unwittingly give you the wrong impression about how worried you should be about things. They don't mean to do it I would say in most cases, it's just that English is not their mother tongue.