There seem to be a few up for sale that are cat S or N - should we avoid them, or is it not a problem?
There's nothing wrong with a repaired insurance write off, so long as any structural damage has been repaired properly. Personally, I would like to see the car before it is repaired, or at least some photographic documentation of the damage and repairs. It helps if you know what you are looking at, as there are plenty of ex write offs out there that are bodged up for resale.
BUT, and it's a big but, you have to bear in mind that these cars are worth considerably less than an unrepaired example. The old rule of thumb used to be that the trade value was halved, but these days they can easily go for 75% and more.
Most insurers have no problem insuring previously written off vehicles, but the insured value will be lower if you are unfortunate enough to write the vehicle off again. A small number of insurers will decline to offer insurance, which may narrow your choice of insurer.
Other half has just swapped from a 2008 mk1 to a 2015 mk2, the premium increase was negligible. A car that is new to you will always cost a bit more to insure, even if it is identical - most insurers reduce the premium slightly the longer you have owned a car. I would guess that the base premium is around the same for both cars, it may even turn out to be a little lower for the newer car, in the long run.