proper car to rent for Naxos interior

We have always rented small cars. Never had a problem travelling in Naxos. I believe rental companies choose their vehicles with sufficient capabilities to drive throughout the island.
Here is another tip, arrange to pick up the car in the evening and then return it in the evening 48 hours later. We have found that picking the car up in the morning can be a rather slow process and we often wasted the first couple of hours getting the rental on the road. If you pick up in the evening you can be off as early as you want next morning.

You're welcome, dd65. :))

Car rental companies usually have a classification starting from category A, then B, etc etc, mais I also look at the engine power (in cc)

The A categories are mainly 1100cc and the B category more often 1200cc (but it's not a rule)
These few 100cc can make the difference in a mountainous environment like in Naxos.

In my opinion it's useless to take a higher category but it's up to you.
For a few years now, I prefer to choose in category B with 1200cc because, if it can be fun for 10 minutes to drive at 20mph on sloping roads, it can also sometimes be boring.

I should point out that I'm talking about manual cars, not automatic.

And whatever vehicle you choose, since it is always specified as "similar", expect to get any other car in the same category, but you already knew that.

Stan has a good suggestion about the pick-up and drop-off time. Don't pick up the car too early in the morning, wait until at least noon.

You probably won't be driving a lot of miles but just to warn you that gas is very expensive in the islands, about 2€ per liter (8€/gallon)

Thank you, both. We were at first going to follow stanbr's idea of renting the car the night before we need it, but DriveTime can bring it right to our apartment in the morning, and then we can return it at the airport two mornings later before catching our flight out to Athens. (The apartment claims there's parking 328 feet away.) This seemed like a good way to easily get to the airport - unless y'all know any reasons why that's not such a great idea...
And, JoLui, we will be renting an automatic. We both do drive stick as well but figured, given very windy unfamiliar roads that get quite steep at times, we'd be best off keeping things simple.

The maximum elevation on Naxos is 3200 ft.

Any car a rental car company has in its fleet can make it up any paved public road you might encounter.

We rented a cheap car to visit the beaches in Naxos but thought it would not have enough power for the mountains and rented something else for that. We then saw the car we had rented the previous day in the mountains.....

Thank you joe32F and BethFL. I think we're going to switch gears (no pun intended!) and stick with the small car. I appreciate your input. However, we'll switch to doing it through booking.com, since that will be less expensive and, hopefully, will allow us to rent the car in the morning (at the airport) without a huge delay.

I hope that last thought is accurate.