ok I'm back!
Teddington - I think if you can afford it, Teddington will give you everything you want. Loads of trains into central London at peak times (though no trains round here are quick - it's like a tube, they stop everywhere on a massive loop line!). Schools are brilliant - any primary school in Teddington is good. M&S on the high street, Tescos, swimming pool, lots of sports facilities, Bushy Park, lovely walks by the thames, footbridge to the other side of the river and lovely walks to Richmond Park, Kingston v close for shopping. V villagy atmosphere. Teddington is also chocca full of young families so loads of play groups etc.
Hampton - is not on the main loop line (that Teddington, Kingston, S Hill are), it's on the Shepperton line which means the trains don't run as frequently. Some lovely schools, really lovely villagy feel, Bushy Park, lots of small shops, huge Sainsburys, v close to M3, Hampton Court, river - again lots of young families so lots of playgroups etc. One of the other (few) downsides to Hampton is that the secondary school there is not that well thought of - I am sure largely because Hampton School (private boys secondary) and Eleanor Holles (private girls secondary) take a lot of the pupils at secondary level.
S Hill - on the same train line as Teddington and has good schools nearby but with S Hill it would really depend on whether you were closer to Tedd or Twickenham in terms of what shops you get etc.
Property price wise - S Hill and Teddington will probably be much of a muchness. Hampton will be slightly cheaper.