Moving to Algarve. Please help where to start.

I moved from UK to Portugal - Albufeira - beginning of 2019.   Applied and was granted Residency and Non Habitual Residency also.
It is relatively easy if you are an EU Citizen but please check IMMEDIATELY if you ought to register anything before end of year in 48 hours.
Visit SEF website for some advice.
To register your residency, simply take your identification documents and register an address in Portugal.
This could be a purchased or rental property, or even a camp site!!!
In my case the local Fincas Office (where you visit to register) did not ask for evidence of rental property!
Once completed, you then visit the local council office for some verification and then back to Fincas office.
You could do all in one day.
As for schools, I have no children but I would guess, once more, the local council office is where you register.
You will possibly need an Accountant to complete your annual tax return unless you are fluent in Portuguese, but that can wait until Spring or Summer 2022.
Remember Portuguese tax year is same as calendar year although you can backdate your residency depending you register before end of March (I think the date is).
I would recommend purchasing a "Living in Portugal" guide from Blevin Franks website for under 10€. It was very helpful and it will give great guidance and easy to read and fallow.
Hope this helps.
Alan.

I hate to swear but Brexit will have made it a lot harder for you. It will not be impossible. But you will need to do a lot more homework. You have to remember you will no longer be an EU citizen but a 3CN so will need to have a visa etc.... I recommend you contact the Portugal Embassy to ask what the requirements will be.

If you are on Facebook join-
British In Portugal group which is part of British in Europe
Website - British in Europe

Good luck