I know it's all extra cost, but as inner tubes are cheap (about a fiver each) I'd buy a couple of new ones anyway. You almost certainly won't have to but if you do you can keep the old ones on you as spares and carry them with you. At some point you will get a puncture and if you have a spare tube on you, and a pump of course, then you'll be able to change it at the roadside and be back on your way in a few minutes.
I just checked on
CRC, only £2.99 each for tubes:
http://www.chainreactioncycles.com/Categories.aspx?CategoryID=184
Don't be scared of changing a tube either. Practice at home first. At some point you will get a pucture and if you know how to change a tube you'll be fine, if you don't you'll be stuck at the roadside. It really is very simple, even I can do it in ten minutes! Carry a few disposable latex gloves with you to keep the muck off your hands and a small pack of baby wipes to clean off any that does.
As for tyres - personally, and only personally, I'd keep to roughly the same same size. You probably have something like a 26" x 2.0 or 2.1 tyre now? If so I wouldn't go smaller than 26" x 1.75 but that's only my opinion. If nothing else a MTB looks pretty silly with skinny tyres fitted
But then I'm vain!
Last of all - don't be afraid of asking any questions at all on here. Nothing is too basic or silly and we were all where you are once.
Best of luck.