I am trying to decide between car and train/bus. I'll be in London, take a train to Portsmouth. Then, interested in seeing Arundel, Tonbridge Wells, Sissinghurst Castle/Gardens, Igham Mote, Pensworth Place (?), Deal and Sandwich. What is the best site to look at to figure out bus/rail connections, to plan the journey? Thanks !
Try Traveline.info. My gut feeling is that you might be better hiring a car.
Traveline, as noted, is very good - but a teensy bit fiddly - for working out buses. For trains I prefer http://www.nationalrail.co.uk/ for the reams of data available. For visiting the sorts of places you are, in Kent and Sussex onwards to Portsmouth, especially visiting National Trust properties which tend to be somewhat remote from train stations (even though there are hundreds of train stations) I'd probably go with a car. The countryside around there is fabulous. A car would allow you to stop and smell the flowers and stop at other National Trust properties as you come across them.