We always go the first week in October. Last year it was hot and sunny every day - perfect temp of about 25/26 - shorts and swimsuits all day and just a light cardie needed in the evenings. The average in mid-October is about 22 I'd say, with if you are lucky, only a few showers.
Lagos is very nice - with a beautiful, if small, beach, Praia don Ana (and others nearby) but in my view Albufeira is a little more fun and in October will not be full of mad party-goers. If you go there, AVOID The Strip end except for a quick look perhaps, and stay in or near the Old Town which is full of charm. There are some lovely beaches along this part of the coast reachable by cheap local bus or car.
Albufeira.com has lots of useful info, links to official weather forecasts, a webcam onto the beach, and a forum where knowledgeable people will answer your questions. A useful starting point even if you decide to go further West, Lagos direction.
Loulé is a well-known inland shopping town, quite sophisticated, with weekly markets (some good, some rubbish); Silves, also inland, has a lovely castle and is worth a visit. Both places are easy to get to with a local tour or by car.
If you decide on Lagos, most people seem to visit Sagres which is the extreme Western end and from where the 15th century navigators set out.
We leave for Albufeira tomorrow but unfortunately the weather has taken a chancy turn with showers and storms. It will be much warmer than the UK even so. Hope you have a nice holiday!