UDP/TCP hole punching vs UPnP vs STUN vs?

I'm trying to make a P2P Program and need help with getting through the NAT of the clients. I'm curious about:

1. The drawbacks/benefits of the three methods i listed and which else exists?
2. How many routers support which methods?
3. Which methods are commonly used by the big companies? (BitTorrent, TeamViewer,...)

UPnP requires software support in your router. Even when routers have it, it's sometimes turned off due to security concerns.

STUN uses a simple public server to detect the presence of NAT and the real IP addresses. This is useful for other, higher-level protocols that do the useful work.

Hole punching is a simple technique to connect two computers. It requires a 3rd public computer to communicate between the 2 computers behind NAT. You could run your own server with a custom protocol, our you could use STUN and existing STUN servers. (Only a few packets are needed for setup, the rest are peer-to-peer).

Of course, some NAT firewalls are incompatible with the above, so you may need a custom protocol. Bittorrent does this: they use different techniques depending on which clients are behind firewalls and whatnot.