Traveling to Algarve

Renting a car once you get to the Algarve would be a better plan. The buses and trains are not a great way to get around the area. The trains will get you to the towns, but the buses are infrequent. If you are scouting for a potential move, you are very unlikely to be able to live comfortably in the Algarve without a car.

Yes, I get the idea. But we've heard of a lot of crazy drivers in Algarve (is it true?) And we don't know much Portuguese, so might have trouble driving with signs in another language.
Also is there way to get from Lisbon to say Lagos or Portimao and stay in each town for 1-2 days
moving gradually west to the Spanish border?
Or staying in the center (Faro), doing daily trips to the cities west and east is better?

You won’t find crazy drivers. The roads are good and not overly busy. You only need to look out for place names on the road signs but use GPS and you’ll be fine. It’s a very easy place to explore by car.

Renting a car one way across the Portugal-Spain border can be expensive costly. We found the ALSA bus and Flix bus the be fine from Seville to Algarve and Algarve to Lisbon. Uber works fine locally in Faro, Lagos, etc. but not west of Lagos.

Portuguese drivers can be a bit wild but not like Italy! They do like to honk their horns a lot!
You don’t need to know Portuguese to drive in the Algarve or any place in the country. Signage is very much like in the States. And, everyone in that area speaks English.

You can stay central and take trains to other areas but it will be slow and the timetables might not fit with what you want to see. And, yes, you can also stay shorter times in a few towns moving eastward. But, changing hotels every 2-3 days is a pain, IMO. And, once you get to those towns, you will need to get around so might need taxis or Uber.

I would suggest taking the train to your first destination in the Algarve, then renting a car for the time you are there. Drop it off before coming back north. Especially if you are considering a move, take the risk to drive. It would be the first of scary things associated with moving here!

Some years ago I 've spent 14 days in Faro and Lagos to see by train, ferry or bus: Faro old town and churches, Estoi, Loulé market, Albufeira (Praia da Falesia), Tavira and the islands, Portimao, the wonderful beaches and town of Lagos, Sagres.
Quarteira is ugly, Vilamoura only interesting for golf experts.