@dianegrahamjohnson
Welcome to the expat.com forum, and good luck with your potential move to Sunny Spain!
It's a beautiful country with lots of very nice places that you could settle.
Location: I recommend looking at Idealista (dot com) which is a very large online property agent. They have lots of listings (to rent and to buy) all over Spain. This lets you check what kind of property you can get for your budget in any town.
Rent/Buy: I think many would recommend that you rent to start, so you can check out a particular area. You might even do short-term rentals (Booking dot com) for a few days in several places, to get a flavour of different parts of Spain. Or, if you find a place/property you love, you can buy immediately. To buy, you need a NIE (identity number). Spain uses a notary system, rather than solicitors. The cost of purchase varies, but my ballpark guess is 15%-20% on top.
Transport: Having a car is very nice, I like having transport. However, in Spain we don't have a car. If you chose to be car-less, then it's usually easier to be in or near a larger town/city. In our case, we live in Elche, which is a typical Spanish city just outside Alicante city and the Alicante-Elche airport. We have an apartment in a nice part of the city, within easy walking distance of the centre and our local Lidl. This is big enough to have all services, and we find it extremely convenient. Even if, longer term, you want to be car-less, the initial location/property hunting will be a pain in the proverbial unless you have a car.
Residence: The No Lucrativa Visa (NLV) is the most popular option for retirees. The process, at your Spanish Embassy, is usually fairly straightforward, and all the requirements are listed online. Pension required is about 2,500 euros per month, or you can show savings instead (just under 30k euros).
Tax: If you live in Spain, you become Spanish tax residents. If you swap the UK for Spain, then I doubt it's a big deal as you'll probably pay a similar amount of income tax.
Banks: You can keep your UK bank, and open a Spanish account to make regular transfers to. Or you can use an account with an ebank/emoney option like Revolut or Wise.
Healthcare: Before leaving UK, get your EHICs/GHICs as these are useful abroad. Also get your S1 forms as these are certificates of entitlement to public healthcare in the EU. Then you can register in the Spanish public healthcare system. It's broadly similar to the NHS, but some folks would say it's better.
Dog: It's totally doable to relocate with a dog. Regardless of his feelings about cars, I would say that Spain is a very manageable drive, and easier than flying with pets. And you get to travel with a load of your stuff. Hot countries have their challenges, but also manageable. We always carried plenty of water and went for walks in the early morning or late evening when it's cooler. Probably, just like people, he will appreciate the AC in the hotter months. :-)