What inner tube do I need for this tyre?
Looks like 28 x 1 3/8 (although I did have to squint a bit!), or 700 x 35 if you prefer metric. I think they're pretty standard, I seem to remember having a hybrid that had this size wheel.

For example, the first result on a google search shows one on Amazon. That particular one is a Kenda but I'd lay odds that all the main manufacturers will make this size.

As regards an on-the-road fix, I carry a repair kit (glue &amp; patches) but to be honest would only use if absolutely necessary. Its pretty cheap, and certainly easier, to carry a spare tube. That plus a couple of levers, plus a small pump or CO2, should get you home. I like to carry some disposable latex gloves as well, just to minimise how mucky I get.

If you start getting regular punctures, look more at what tyres you're riding.