A lot of cameras have gotten quite a bit faster over the years. Try for instance a canon Powershot A610/A620. They have the specs you are looking for and I believe they are quite fast in focussing, reducing shutter lag. A trip to a shop that carries them will clear up fast enough if they are fast enough for you.
Canon EOS 350D, Tamron SP AF 90mm F/2.8 macro, Sigma 18-50mm F2.8 DC EX, Canon EF 70-200mm f/4 L USM, Tokina AT-X124 Pro 12-24mm F4, Soligor 1.7x C/D4 DG Teleconvertor, Manfrotto 724B tripod, Canon Powershot S30