Beach/touring hols

Having decided to take my son to Portugal for a much needed rest (he is a chef) I'm undecided where we should go. I will be flying to Scotland where we will take a flight to Lisbon (or that was the plan) for 5 days and then on to a beach area where he can relax near a pool/beach. We will have about 12 days (the remainder will be spent in Scotland for the beginning and end of our journey)so: do we need to rent a car between Lisbon and an unknown beach or is public transportation available? Which beach apt. or hotel is recommended? I am thinking the middle of September on. Unfortunately, have not won the lottery so finances are a consideration as I do need to to get to the UK before we start this adventure. that being the case, all advice from savvy travelers is welcome!

Cheers,

Sophie

Double post. See the other answer.