Have a look at my 'Twin Reverb' tone here - http://www.joesjamblog.com/tones4.html which will get you in the ballpark for the amp sound. The Ventures used Fender amps (Bandmasters, I think).

The original "Walk Don't Run" lead was played on a Fender Jazzmaster by Bob Bogle, not a Stratocaster so the sound is a bit fatter - but not as fat as a humbucker. The Strat neck pickup would be nearest. The Ventures later moved over to Mosrite guitars which have P90 type pickups - close to the Jazzmaster pickups.

http://www.youtube.com/watch?v=lJ11y7pYl-8&feature=player_embedded#fmt=18

The 'singing tone' is obtained by riding the whammy bar to get more sustain but most other guitarists would use (left) finger vibrato to get the same effect.