Hi EdN,
I cycled via algarvinia in 2012, starting in Alcoutim on the Spanish Border & with a group, using MTB's we took 5 days to reach cape st vincent. I was not involved in the organising, but the accommodation was pre-booked & if I can remember correctly only one night was spent outside of a built up area/village. Terrain was not to difficult, at the beginning we had quite a few kilometers of sandy, lumpy terrain, there were beautiful forests & streams with only a couple of scenic mountains to get over, biggest being Monte Chorro (I think). It was hot, damned hot, but then it was early September. Agree with other posts, beautifully friendly people & very cheap. As I said it was 8 yrs ago & from what I've heard a lot of work has been done on the trail since, but at the time we may have run into trouble without a Garmin (trail markings sparse at times). I've since done the Frances & La Plata - although as beautiful, the algarvinia is much, much less commercialised. I'm sorry I cannot be more detailed, but I do believe there is a lot of information on this trail online. There are also your groups for this trail to organise your accommodation & forward bags. I would not recommend to an inexperienced hiker, If you choose to go be prepared for days where you won't meet a soul, but most of all enjoy & stay safe.