Wider tyres have fewer punctures because they can be ridden at lower pressures and roll over rubbish more easily rather than getting punctured. Also, they have fewer snake bites. The argument in favour of them is all the stronger on a towpath: get the widest tyre that will fit your frame. On such surfaces wider tyres are also faster.
Personally, I would use the Conti Topcontact Winter ii in the cold season, and something like the Marathon Racer or Big Apple in the summer. These are the tyres that we have used in our family on our commute bikes, and for all four of us together we average something like one puncture every few years. Admittedly this is in Holland, where the streets are much cleaner. On my own commuter bike I even use the quite fragile Panaracer Pasela Tourguard, and have not yet had a puncture in four years, and that in a student town.
What I have noticed over the years is that it is worthwhile to replace tyres well before they are completely worn. Also, cheap tyres even from major brands are far more puncture prone than the top models.