You can use any navaid you like, enroute.
Correct
You don't need an alternate just because the destination only has a GPS approach.
Are you sure. I think a tech alternate is require for a destination with only one type of approach available.
VOR approaches are available all over the country.
Hmmmm, last time I checked there was a fair bit of the country with no VOR coverage. Everywhere north of AA, all of the West Coast of the South Island for starters. Quite a few places in between.
The nav aid you'll most likely use the least until you score a Link job will be the ILS. If I was leaving any nav aid off the list to start with it'd be the ILS.