Type of car to rent for touring

Range Rover is the obvious first choice. The diesel model of course. If that's too big look at the Range Rover Sport.

The OP is asking for advice to help choose between economy or mini class for a car rental to tour Ireland. James E is recommending a Range Rover. The Range Rover is an SUV and an awful lot of car for his needs, to say nothing of the expense.

I've never regretted going for the smallest car we could tolerate. I was thankful for it many times when meeting iron elephants (tour buses) around a blind corner on a narrow road. I'm not sure what you mean by handling distances other than the "tolerate" factor, they are certainly capable of driving distances. Also, you're probably going to do most of your driving on smaller "N" and "R" roads. I've had them for 2-3 weeks at a time with no problem. The only negative was getting some sort of Suzuki a couple of years ago that was very spartan in equipment and had no way to plug in external music, 10 days of listening to RTE all day grew a bit tedious (but was entertaining and informative in small doses). I usually strongly prefer a manual transmission, but have decided against it in Ireland, but given the extra cost (nearly double) for an automatic I will likely go for the manual next time.

The economy car options are fine. I had a mid size on my last visit and it was too large IMHO. Caused some consternation and angst on some West Coast roads. No harm, no foul but shouldn't have agreed to the free upgrade. BTW if you don't already do this take snap shots with a camera or on your phone before and after you've driven the island. Always help to document what the car looked like when rented and when its returned. Visual proof in case there's a claim of damage. I've driven the island 3 times now. Take it slow, watch for sheep, bikers, pedestrians, lories, farm equipment and rainbows ! Beautiful country. Enjoy it!!!

Norma, you are correct, but our Jeffries has been with the family since he took over from his father. Jeffries feels more comfortable driving the larger vehicle so we try and accomodate him. Personally I prefer the smaller, classic, more eco-friendly XJ6, but they just aren't available any longer and the new replacement just doesn't have the same ride.

If you're already familiar with driving on the left then you'll be fine.
On our last trip we at first opted for the smallest vehicle we could get, knowing that our first two vacation rental cottages were way off the beaten path. The "roads" were narrow to the point that we had foliage scraping both sides of the car as we passed, so the small car was the best choice.
For the second month of our trip we were upgraded to a mid-size (a Peugot I think) and it was wonderful. The comfort and generally improved road handling made for a much more enjoyable driving experience, but that was mostly on the N and R roads. So, unless you plan to go way off the main tracks I'd suggest that a mid-size vehicle such as one of those you propose might be your better option.
Many of the rural roads are only one lane wide anyway, requiring drivers to use the frequent pullouts to allow opposing traffic to pass, which you'll have to do whether you're in a mini or a truck. The Irish drivers are used to this, and in fact had usually already backed into a pullout before I even had time to think about it.

Droll, James E ...... very droll.

Norma, I will accept that as an adjective.

For those for whom English is a second language:

droll
/drōl/
adjective
adjective: droll; comparative adjective: droller; superlative adjective: drollest

1. curious or unusual in a way that provokes dry amusement. "his unique brand of droll self-mockery"

synonyms: funny, humorous, amusing, comic, comical, mirthful, hilarious;

I will add that I have only driven a car once while on vacation. It was in one of those countries that drives on the wrong side of the road, in one of those backward constructed cars. It was a disaster. A long line of parked cars ended up needing new side view mirrors as did the rental I was in. Now I leave the driving to Jefferies.

Downton Abbey has had a strange effect on some people.

I've always requested the Economy class as a solo traveler, since the price difference versus the Mini class is often just a few dollars. And somewhere in the back of my mind, I believe that I'm getting a more powerful engine, as well as better likelihood of a trunk/hatch area with a hatch cover, rather than one that's exposed.

Norma, you too? Here I thought I was the only one. You are indeed a great sport. Don't forget that I still owe you that tour (we walk or Jefferies drives) and roof over your head.

I was upgraded to an automatic Peugot SUV because the little manual car I had reserved had a broken GPS. I had to contain my self when saying "yes, that would be fine, thank you." What a great car! I put 2k miles on it in 2 weeks, and would have been happy to bring it home.

Two years ago in Ireland, we got a free upgrade to a BMW. Extremely comfortable and drove beautifully. No surprise there. However, it made for some terrifying moments on extremely narrow secondary and tertiary roads on the west cost. This year, we're an automatic transmission version of the smallest car available. It's about 6" narrower than the more popular cars and we will love that. It should be plenty comfortable for just the two of us.

Thanks for the suggestions. I decided to get an economy car because of the price; it should be fine for small roads, and it's not much more than the mini.

Good decision. The smaller the better as long as you can fit your luggage in it. I prefer automatic but if are used to manual it will save you some money.

Get as small as you can. Irish roads in the hinterland are really narrow and several bridges are one-way, as are some of the roads.