Having looked at inner tube sizes it seems they typically cover a 0.5" margin of inflation, so I assume my tubes are something like Kenda 1.25 - 1.75. Could they safely be inflated past that to 2, if I'm to keep them as spares?
+ 1 to Jur & Thor on above. Getting Schwalbe tyres & tubes together is best.
Do you want the big apples for a more more cushioned ride? If so they are great for that. If not I recommend the Marathon Plus for its excellent puncture resistance and strength. Still rolls very nicely too. Got them on ym 20" Downtube FS. See: Upgraded (modded) Downtube FS 2007
I replaced the Swift's kenda kwest 1.5 with a Schwalbe Big Apple 2.0 without replacing the kenda's inner tube. The tube was rated 1.5 - 1.75. It's been two months now and it's still going strong. Some people said the Big Apple 2.0 is more like a 1.75.