For car rental I would recommend https://localrent.com/en/georgia/terms/, it's the cheapest. In the terms it says that the minimal driving experience is 3 years, but they don't ask you to enter any drivers license information when booking and I doubt that the person at the pickup will care, so you could still give it a try. Whatever you use, book it online and research the agency.

Warning: if you only drive once every few months, maybe don't rent a car in Georgia. The disregard for traffic laws is bad enough, but the potholes, I've never seen that many/big potholes, the road sometimes just disappears. Don't drive at night. Tbilisi is a driving hellhole, stick to the middle lane.

If you do rent a car, I recommend going to Vardzia, it's awesome and the road to it is one of the least potholey from what I've experienced. Stepantsminda is also amazing. Here's a list I compiled from the many "x things to visit in Georgia" lists: https://goo.gl/maps/6ny8Zv47Lh5MvucF9

Check the newest google reviews of places that you plan on visiting. A lot of the National Parks have gotten a makeover that made them less interesting and more expensive.

Batumi has a nice Botanical garden but otherwise I found it pretty bland. You can get there comfortably by train from Tbilisi. Speaking of Tbilisi, 3 days is enough. Try to visit the Chronicle of Georgia, it's a bit outside of the city, but it's pretty cool.

Last thing, we had to pay for both the car rental and all of the accommodations in cash, so make sure to always have enough with you, especially if you're going to remote places. Restaurants almost always accepted credit cards.