@shelleyadrienne
A new adventure! Good luck!
1. As many of our knowledgable members here have confirmed, it is more difficult for Brits to move to Europe post-Brexit. But, as a retiree, it is possible for you to get residency, and it should be relatively easy (and the process would be similar for any EU country that you chose). It would be granted on the basis of your pension, rather than your ownership of property. Therefore, you might want to consider getting your residency sorted out before choosing a place to live. Especially as you'll have to be present in the country to apply for residence, which is a great time to look around at the country, and particular properties. But either way would be OK.
2. I am one of the expat.com posters who has purchased sight unseen, via the internet. Indeed, I'm writing this from our house in the Balkan Mountains, which we bought without viewing in 2018 - and it's wonderful! So it's certainly possible. However, most here would suggest you avoid doing so, and even though I've had good experiences, I certainly wouldn't recommend it. If you decide to do it this way, you must be careful because there are many potential pitfalls, both with the property itself and the transfer/purchase!
I bought from Ebay sellers with very good feedback, and I also purchased a property via a very large, reputable estate agent. I would say that reputation of the seller/agent is a huge factor in a remote sale. Because of the Covid Crisis, it has been much harder to travel, and hence many agents have been using the internet more, so that you can feel more comfortable buying remotely. They take lots of photos, include videos of the property, and some even add interactive 360 degree views of each room! Some are conducting "virtual viewings" where they walk around the property while on a Skype or Whatsapp call with you. In this case, we might feel it's almost as good as being there in person.
You can also use Google / Google Maps to look at the village/region and do research on the immigration rules, the cost of living, and the experience of other expats/retirees there.
Besides, you don't have to make a final decision. You can use the above methods to create a shortlist, then only go view your top choices. Or, possibly, if you love a particular property, you can pay a small reservation fee... and then view. If you see it and discover something unexpected, and feel you've made a terrible choice... it's probably worth losing the reservation fee rather than going through with the purchase.
3. Separate from viewing and choosing a property, you have to buy it. Most European countries use the notary system, where buyer and seller meet at a public notary and sign the notary act. You can do this while still in the UK by giving a POA (power of attorney) to a trusted friend/agent/attorney, and they can sign on your behalf. Such a POA is a formal legal document, so you need the correct version for the country of purchase, and then you need to get it (a) notarized, (b) legalised, and (c) sent over to your representative. You don't need a lot of documentation to buy a property: your passport, and the money, will normally be sufficient!
4. Italy and Greece are beautiful countries. There are many happy retirees here. Perhaps also consider Spain and France because these have also been very popular with Brits. I have personally lived in France, Spain and Cyprus, and very much enjoyed my time there. If you have a generous private pension, you can live anywhere in Europe. However, if you only have your state pension, I think you might find things a little expensive. In this case, I suggest you also consider Bulgaria, which is substantially less expensive to live, and has cheaper property. I am now living here mostly, and I recommend it highly!