Expanding on Pnorkle's post, I would suggest a multi-tooth hole saw, or one of those carbide encrusted hole saws for drilling through tiles. A single tooth cutter will be a recipe for a broken wrist when it grabs (and it almost certainly will). As stated by others, run as slow as possible.
Heat is your enemy when it comes to stainless as it work hardens rapidly. A stream of water is better than nothing at all, but a regular squirt of soluble cutting oil in a squeeze bottle will be a good option. The best cutting compound I have used on stainless is Rocol RTD. It is expensive, but it is by far the best cutting liquid I have tried over the years I have machined stainless. It can be had in a paste or a liquid. Smells revolting, so you know it will do a good job. You may need to stop regularly while drilling and cool the site down, even when using lubricants. If water sizzles on the metal, it is getting too hot.
The other thing with stainless is not to use blunt tools or allow the tool to rub without cutting. It will work harden in seconds. If you can strap the pot under a radial drill and use the hole saw there would be safest (friends with any engineering shops?). If you were really stuck, you could mark out a circle and drill a chain of small holes around the inside of the line so that you can break out the slug in the middle, then use a carbide burr in an air die grinder to grind out to the line (with care). Again, you must use sharp tools or the stainless will punish you badly. If you have to drill with a hand drill, I would suggest clamping the hand drill on its side to a large block of wood or such and have the pot clamped down at the right height relative to your drill. Then use the drill and block to allow you to just feed the drill into the side of the pot without trying to keep things square in every direction. Having the drill break through evenly will stop breaking tools or body parts. Good luck.