Although some may disagree, it's generally not worth patching a tube unless you don't have a spare tube handy. However, patch kits are so small and light that there's no reason not to carry one unless you're counting grams. It'll come in handy the day you carry a spare tube and have two flats.
I can't recommend any brands of patch kits, since I've never even used mine. However, I suggest avoiding the very cheapest tubes, such as Forte (Performance house brand), for example. Most flats I've had have been with cheap tubes.
In my experience, keeping your tires properly inflated won't help much with these kinds of punctures. (See the comments for another take on that, though.) I suggest you look into puncture-resistant tires. These are heavier and may slow you down a touch, but not as much as changing a flat will! (These tires still get punctures, but not nearly as often.) I'd also like to mention that I've almost never gotten a flat with tires that have full-knobby tread.
Are you riding on- or off-road?