Depends on your budget!
Maybe ask your printer about "Spinnaker FasTrack"; it's not a vinyl although they do offer some vinyls as well. Vinyl can crack, melt, doesn't always tolerate extreme temperature, and is expensive. Make sure to mention what you want to use your sticker for if you order vinyl! At least the printer will suggest you the right type; mention what are the maximum and minimum temperature the sticker should be able to handle.
FasTrack can be printed with a digital printer for short runs or on standard offset, and it's a very popular stock that almost all printers know about. There's different finishes, adhesive and even colors.
It sticks very well on irregular surfaces, even the surfaces that are not very porous or clean. It's water resistant, very opaque, tolerate condensation, has strong adhesive and tolerates outdoor use very well. For microwave, I'm not certain; contact the company or verify the datasheet. I know it does tolerate sun exposure well though (eg. colors, shape and adhesive)
See links about this for more details on FasTrack:
Commercial alternative to vinyl for bumper stickers and wine/beer/food labels?
You should contact a local printer and ask about your project; it's very specific. Even if they don't print on the stock you need, they will be an intermediary and use another printer they trust for this, and manage the project for you. But I suggest you go see a high quality printer that does 4-6 colors offset at least, not a little print workshop that only has digital or 1-2 colors machines.