4 quarts is not an efficient size generally speaking. Too small. And a big pot can work fine only partially filled.
Many sets come with 4 and 5 quart pots as a cost savings mechanism. But that's small for most batches of chili or soups, but can make for a fine braising pot/dutch oven.
Most here wouldn't consider it a stock pot until it hits 8 or 12 quarts capacity, 12 being the most commonly recommended size. 12 is a versatile size for big things like a seafood boil or turkey stock or whole lobsters.
It takes very little effort to make a bigger batch of stock, compared to a smaller batch so you save time and effort in the long run over little batches. Stock is a basic ingredient in a tremendous range of dishes and critical for sauces so it's always worth having plenty on hand or at the ready in the freezer.
You want a stainless pot with a heavy base over any other criteria. A disk base is fine, in fact all of my stock pots are disk based, not multi-ply clad ware. Nothing wrong with clad cookware, in fact it's a very functional type of cookware, but it costs more. For a stock pot, I don't see any return in performance nor is it worth the extra cost or weight.
There are a lot of worthwhile disk bottomed pots. Most of mine are Tramontina as they're well made and inexpensive. Target's house brand can be a good deal too, Chef's Mate or Chef's Choice I think they're called? Probably the 12 qt would be only on the web site though. All-Clad makes good cookware but you pay a lot for it. Also check Walmart on-line for some good deals on a 12 qt pot.
Yes, even if just cooking for one. It's worth it. And get a dedicated freezer as it's the best friend for cooking for one in managing leftovers and preventing waste.