As far as tubes, there are thicker and thinner tubes, but for most of us, a tube is a tube. Just make sure it has the right type of valve (Presta or Schraeder)

However, I avoid tubes with slime (personal taste) and the ultra-light tubes that racers use to save a few grams, but you won't run into too many of those in 35mm, and they tend to cost more than other tubes. If your area has a lot of goats heads or other thorns, you can use a thorn resistant tube to help a little, but it also weighs more, and some people can tell the difference and feel the ride is sluggish (not me, but some).

For flats, I carry at least 1 spare tube, a patch kit (in case of additional flats), a couple of CO2 cartidges with an inflater, a Topeak Road Morph pump and plastic tire levers. I am over-prepared, but I figure that any extra weight just gives me a little more exercise. I ride some fairly remote rail trails, and I don't want to walk 6 or 7 miles to the nearest trail head (or 10-20 miles back to my car) because of a flat.

Save your Road Morph for emergencies, and buy a decent floor pump to top off before rides. I have had good luck with my Blackburn Air Tower 2 which works for both Schraeder and Presta valves. After several years it just started having trouble with the head, but the manufacturer is sending me a head rebuild kit for free (lifetime warranty).

Since you have been searching, you have probably read it before, but I will add here for completeness... When you get a flat, make sure that you identify the cause so that you don't immediately get a second flat...