Being in average shape is a fine place to begin. You will likely be exhausted during your first class, regardless of shape. It takes some practice to learn how to breathe during warm ups, and most people panic during their first roll. The first time an unfamiliar situation is encountered, breathing tends to go crazy and incorrect instincts kick in. Athletic shape often means doing the wrong thing harder and faster.
Once a basic understanding is reached, you should experiment with athleticism in a safe fashion. This is only one of many factors that takes years to fully comprehend how to use properly.
It may be hard to move on the ground if you’re so overweight that you can’t see your….. feet. A good place to begin is to just show up. Everyone is working on their own goals at their own pace. Good jiujitsu works within natural limitations, and expands into what’s reasonable and sustainable.
Be honest with yourself. Most people use shape and age as an excuse to do nothing. Anyone who has trained in Bjj knows better. You can find people who are out of shape, over 60, or even missing limbs training and sometimes competing. I’m not going to say everyone wins all the time, but everyone does earn respect for being willing to face their fears.