First, let me say, we do a mix of purees (especially naturally "baby foodish" stuff, like applesauce, oatmeal, yogurt, butternut squash puree, etc), plus small pieces of food. So, my way of doing it might not be good enough for someone that needs a larger supply.
If I make a bigger batch of something, I freeze in ice cube trays, then pop them out and store in the freezer. If I only make a tiny bit, and I don't want to freeze, then I'll store it in 1/4 pint (4 oz) canning jars (with plastic lids--I've been canning for years, and I have a bunch). If it's a tiny baby, then I store in Tupperware midgets. They store 2 oz.
If we're going off for a short time (say going to grandma's for lunch), then I'll take applesauce or whatever in the 2 or 4 oz container. If it's for a longer trip, then I use purchased food. It's easier for my life. And, I save and reuse the jars.
I also keep a purchased thing of food in the diaper bag for emergencies.