Getting both "countryside" and "a town with lots of shops, cafés and restaurants, museums" in the same place is impossible. Bournemouth meets your requirements for "big beach, ... town with lots of shops, cafés and restaurants, museums, gardens" and has attractive countryside quite nearby accessible by bus or train (e.g. bus to Studland and walk on Ballard Down, or train to Wool or Moreton for walks), and is close enough to London for a weekend trip. It has frequent trains from Waterloo, or National Express coaches from Victoria. There is a good bus network within the town and some services out into the countryside.
Oyster cards are not usable outside London. Some non-London buses accept contactless cards but on most you either pay cash or buy a daily or weekly pass (again usually with cash, from the driver). Having decided where you are going, look up the local bus company online.