First approach: How much water does the recipe/bag call for? That’s your starting point; add a little bit for the volume of the food, and a little bit to avoid boil-overs. For example, if the meal calls for 12 ounces of water, and you’ve got 3 or 4 ounces (dry volume, not weight) of ingredients, and allow another 4 ounces for boil-over, you’d need a pot with a capacity of at least 20 ounces. This method assumes you’re going to be adding the ingredients to the 12 ounces of water in the pot, and letting the meal “cook” in the pot.
Second approach: Starts the same as before: how much water do you need to prepare the meal? That’s the size pot you need, because with this method, you’re going to add the boiling water to the ingredients and let it cook in the bag, not the pot. So, if you need 12 ounces of water, you’ll need a pot of at least 12 ounces (I’d allow a few ounces for boil-over here, too - call it 16 ounces.)
One big consideration as you downsize pots is your stove. If you’re using a really small pot, make sure it will sit on the pot supports of your stove. Depending on the diameter of your pot, the supports may be too widely spaced to keep the pot above the flame like they are designed to do.
Other pot considerations: by getting a mug-shaped pot, it can double as a drinking cup or a bowl (if someone offers to split some of their food, for example.) If you use the second approach to cooking, you can put a second pot on to heat up, and drink your tea or coffee from it while you eat your meal from the bag. Cooking in the bag also means your clean up consists of drying the pot and licking your spoon (you can dunk it in the next pot of boiling water you make if you want to sterilize it.) Many of us who use this method (and nearly everyone I know does) have a kitchen that consists of a mug-shaped pot of 20 - 30 ounces and a long-handled spoon, and nothing more. Sometimes, I cheat and bring a second 12-ounce cup if I’m making oatmeal for breakfast; I make the oatmeal in the cup and tea in the pot. (Mostly, I bring along an oatmeal breakfast bar, and leave the cup at home.)
Just to give you an example of sizes, I use the MSR Titan Tea Kettle (28 ounces, I think.) Many of my friends use the new MSR Mini Solo cookset (which includes a plastic bowl), the Snowpeak Trek 700 or 900 titanium pot, or a Snowpeak solo cook set (cup and pot.) A fair number also use the MSR Windburner or one of the Jetboil stoves, all of which come with an integrated pot/mug and plastic bowl. There are a ton of other good products out there that work just as well as MSR and Snowpeak. Have fun looking.
When you decide you just can’t face another freeze-dried entree, come back ask about freezer bag cooking. It works just like freeze-dried meals (you add boiling water to the bag of ingredients), but the recipes use a lot of different ingredients. There are a number of people here who dehydrate their own ingredients and have some great-sounding recipes.
I have a "solo" pot that is adequate in volume, but have gone back to my smaller titanium pot (the smaller of the 3-pots in the SnoPeak set- I think about 1 liter?), simply because the weight is not much more and it is so much more useful. Try to wash your face with a solo pot- ugh. I always like my hot drink WITH my meal, so I have a very light small titanium cup. The regular pot is less "tippy" than the solo pot. No danger of accidently spilling my meal.
Also consider how you will pack the pot. My pot very nicely fits exactly over the end of my tent bag so is not at all awkward to pack. When enough food is eaten, I then pack it inside the bear can. Stove and matches fit inside the cup which fits inside the pot along with my foam cozies for my cup.
The small pot is marginally adequate for two people. I usually take the medium pot if I go with someone.
Be sure to take a lid. Boiling water without a lid wastes a lot of fuel. I have "cozies" for each pot made of old blue foam sleeping pads that have worn out. The foam is held around the pot with a rubber band. There is a round cut-out for top and bottom.