What time of the year? I've done a fair number of dives in the algarve but the dive center I used the most 'Atlantic Dive Center' at Albufeira has recently changed hands (try
Phone: +351282587479). I know the new owner -Cristian- who is good but I havn't dived there since set up changed to him.(speaks English)
I can recommend Blue Ocean Divers at Lagos
http://www.blue-ocean-divers.de/, I've used them before and were very good.
With the Algarve the furtherwest you go the better the water, better viz but colder. It is a gradual change from a mediterranean like waters on the east to Atlantic water in the west. My best dives were from the west, by far. In the winter the waters on the west may be a bit choppy though.
Type of life to expect: Octopus, Congers, Triggersigh, Greater Forkbeards, few damselfish, velvet crabs to name a few. It is not the Med though, so waters will be 12-16ºc at the moment, cooler on the west.
Looking at the map Lagos may seem far but with the new motorway it's easy.