To answer your question, I don't think all non-stick are Teflon, that is a brand name, but I don't even think all non-stick is that technology. I'm quite sure that the way non-stick is used is the key to how healthy it is. For one, you shouldn't use pans after they get scratched up, for two you shouldn't use them higher than medium heat. If you are buying these pans, get the kind that are high quality with a very durable coating, and care for them properly.
If you need non-stick, go low tech and get cast iron. If you care for it properly it will be nonstick. They are reasonably priced, versatile for all kind of cooking as well as both burners and oven, and so durable you can hand them down from generation to generation. They are a bit temperamental but that doesn't mean they are difficult to use or care for. And yes they are heavy. I have also heard that they enrich your food with iron but I'm not sure about that. If so, that would be an excellent choice for vegetarian cooking, and also for people who have trouble with anemia.
The good news is, you may even already have one!
In general though, your choices should fit your cooking style and types of food. And you might need to mix and match materials for your different needs. But do keep it simple. Avoid whole collections or sets of pans with pieces that you won't use. Instead, look at the single pieces you really need, and try to get the most versatile pieces, this will save you money and space. Then get the best you can afford, collecting slowly if you have to.