The drive from Porto to Lisbon or the Algarve is no great problem. There is an excellent toll motorway network covering the whole route.
With stops Porto to the Algarve would take about six hours via the toll motorway. (Tolls for a small car would be about € 35.00)
In September/October you will probably have no problem arranging accomodation "on the fly", save in Lisbon should you wish to lay over there.
As regards destinations in the Algarve, I suspect that from your requirements, that Lagos would be your best bet. It's not just that I live here..but it has the sort of mix you describe.
If you want real partying then Vilamoura or Albufeira are probably more suitable. However, bear in mind that by the end of September, the summer is over and the partying substantially reduced.
Also bear in mind that there you are going to traverse some wonderful parts of Portugal. If you chose to take your time driving from Porto, you could visit Coimbra, Figueira da Foz, Nazare, Obidos, Alcobaça, Batalha, Sintra.
Porto and Lisbon are also great places to visit.
