There are a few different reasons you could be getting recurring flats. The most common is that your tires don't have enough air in them. Then when you start to ride the bike, the tire fully compresses and your inner tube gets pinched between the road and the metal wheel. This is called a pinch flat. To stop this from happening, just make sure you keep the pressure in your tires up to the spec printed on the tire sidewall. Bike tires are just like party balloons - they lose air naturally, whether you ride on them or not. I lose a little over 10 psi a week.
The second most common cause of recurring flats is when you don't remove the cause of a puncture. If you get a thorn or small piece of glass in your tire and get a flat, when you change the inner tube you need to make sure you get that thorn or whatever out of your tire. You can do this by running a rag (not your hand, unless you like cutting open your fingers on sharp things) around the inside of the tire while the tube is out. Make sure you go in both directions. This should snag on anything sharp poking through, and then you can finish the job with a pair of tweezers.
The final thing, which most people don't know to look for, is a damaged rim strip. Do you see where the spokes go into the rim of your wheel? There are holes that go all the way from where the spoke enters the inside of the rim, up to where the inner tube sits on the outside of the rim. These holes are sharp, so they need to be covered up on the inner tube side, or else the tube can get cut.That's what the rim strip does - covers the holes to protect the tube. If you can see any part of these holes when your inner tube is removed, that's a problem. If your rim strip is broken altogether, head over to the bike shop and get a new one, or if it's just shifted over a little bit you can probably move it back into position and everything will be fine.
As far as brands of inner tubes, honestly they're probably all made in the same factory somewhere in Taiwan. The only thing I actively avoid are tubes advertised as "flat-protecting", whether they're that nasty green slime stuff or just extra thick rubber. In my experience, none of that stuff really adds any protection. The slime leaks and gets all over, and anything that gets through the hard rubber of your tire will make it through a soft inner tube just fine, no matter how thick it is. There's also a few different brands of
foam inner "tubes", which are some fancy closed-cell foam things you use in place of a traditional tube. I don't have any experience with these, but I have heard that you can damage the foam by hitting potholes or curbs. Not something you want to worry about with a $20 tube.
I buy all my bike things from my friendly neighborhood bike shop, on principle of supporting folks who support the sport. I don't remember the last time a big-box store did anything for cycling, but I do appreciate every time the local shop gives out free bike route maps at our weekly farmers' market.