To me the "Surf" sound is single coil bridge pickup, a little bit of a twangy clean, and maybe some tremelo. I don't know very much about typical surf music though.
yea deff. the bridge pickup and keep it pretty clean. you can get away with a bit of overdrive but you wanna keep mostly a clean tone. i like a bit of overdrive...sounds better with my guitar. if theres a minor chord like Am, do a little pushing on the whammy and it gives it a nice surf feel. use it like at the end of a song or before a break or something like that. tremlo picking as well, not to fast though, and usually the songs are pretty basic, not to complicated with the solos either. not really my style but that what i can think of from the stuff ive heard.
Twang and reverb! huzzah!

In terms of construction, the riffs are somewhat melodic (most songs are instrumental as well) and fairly repetitious. Pick near your bridge, as well.
Don't tell me what can not be done

Don't tell me what can be done, either.

I love you all no matter what.
I would recommend getting a nice clean Fender amp with Reverb. The reverb on Fender amps sounds so good, it's sexual. But yeah, for a surfy sound, mellow single coils and reverb will get the job down. For a guitar, I'd recommend either a Strat, or even better, a Jazzmaster.
yes on reverb! the old-fashioned spring reverb like they had in Fender amps...