Reusing an old tube only makes it more prone to flats if you go to a significantly larger sized tire and the tube is stretched thinner inside the tire. Tubes don't see the same exposure to the elements that the tire does, and they tend to be OK even if you leave a bike sitting for years and years and the tires are all dry rotted.
As for tires, my favourite is the Panaracer Pasela TG 32mm. Light, good flat protection, rolls nice, and has a flexible enough casing that it feels like a much more expensive tire than it actually is. I get about 3000 miles out of one in the rear.
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"I feel like my world was classier before I found cyclocross."
- Mandi M.