With Avis, you can only buy or decline insurance for the full rental. You cannot get insurance for only specific days. Otherwise, you could only get insurance for one of the days and then try to claim that the car was damaged on that 1 day. Your word vs theirs...

As for picking only Avis or Hertz because of reputation: I'd throw that by the way side. Rental car companies typically have poor customer service and it's not worth picking for "reputation" unless one is much worse than others at your specific location. I'd either pick based upon total price (including taxes/fees/insurance) or because one has a specific car that you want to drive and they confirm that's the one you'll get. Otherwise, price rules in my book.