Sign up. 1i f it is a good school it should scale things for you. 2 If you wait till your fit enough you will never start. 3 without training MMA you will never be fit for MMA anyway. 4 fighting is fun.
As for what you should do extra I would say sign up, wait a couple of week and see how you cope with the demands of training. From there decide how much extra training you want to do. As for the specifics I will let others comment.
Vinyl is fine if it is just going to be you and perhaps a couple of others using it. A bag is a great tool, you can hang it and hit it, ground and pound it, practise transitions on the ground with it, tie a rope round it and practise transitions to arm locks, put it in your guard and move it around, throw it, supplex it, clinch etc etc. You are only limited by your imagination. My most used bit of training kit I have at home is my bag, and I don't even have anywhere to hang it.