My own favorites are Swiss, Havarty, and Gouda. I just finished eating some home smoked Gouda a few minutes ago. Start with a high-quality cheese, whatever you choose.
I only smoke cheese when it is really cold outside, so my cheese does not melt even a little bit. I use the tin can and soldering iron smoke generator in my WSM.
It does not take long to smoke cheese. 60 to 90 minutes will do the job. But, you need to wrap it up and let it sit in the fridge for at least a few days, or better yet, a week or two, before eating it. The smoke flavor needs to mellow out. If you eat it fresh from the smoker, the smoke will overpower the cheese.
I vacuum seal my smoked cheese for a couple weeks.