26" tyres from your local supplier will do very nicely

.
Seriously, you'll need something wide for those rims, Sheldon Browns guide (scroll down a bit
here) should guide on what width will fit.
As for 'puncture proof' it doesn't exist, but some are more 'puncture-resistant' than others, the most resistant usually being said to be
Marathon+.
Just be aware the more resistant, generally the heavier, less compliant and comfortable they are. The M+ are a bit wooden, but they'll last forever and I spit in the puncture fairys eye and don't bother taking a puncture kit with me when out on that bike. On the other hand if you're switching from knobblies on road probably anything will feel like an improvement.