You might want to have tubes with both Presta and Schrader valves (to match the existing tube on the other tire). Theoretically you could use either, but some rims might have a hole that's only small enough for a Presta valve (so I guess that makes Presta slightly more compatible in an emergency!).
I agree that there's flexibility in the sizes. When I wanted to stock up my work's garage with spare bike tires, I got four kinds in total (basically a small Presta, a small Schrader, a large Presta, and a large Schrader). This officially covered pretty much every common road and hybrid or mountain bike with something that was officially rated or matched to it. But yes, as far as I know, one could probably get by in practice with fewer than that and use things that are officially slightly mismatched.
Specifically, I got the Specialized "Standard Schrader" 700x20-28c and 700x28-38c, and "Standard Presta" 700x20-28c and 700x28-38c tubes (the smaller ones more likely for road bikes, the larger ones more likely for mountain bikes). These are about $8 each in the U.S., so a total of about $32 for the set of four. 700c is increasingly common, although there are several other diameters that have been or are being used.
Just having a bike pump can be pretty helpful in many circumstances!