Hi there! My chain settings for classic 60s surf are, for instance (using the Fender Collection series 1):
1) Fender Tape Echo > Amp > Compressor > Tape Echo (Rack)
2) '63 Reverb Tank > Amp > Compressor > Tape Echo (Rack)
3) Tape Echo > Amp (Reverb onboard) > Compressor (Rack)
4) '63 Reverb Tank > Fender Tape Echo > Amp
5) Compressor > 4) '63 Reverb Tank > Fender Tape Echo > Amp
The Amps: I find that Deluxe Revb., Twin Revb., Vibroverb Custom (Stock mode ON) and Princeton Revb, fit perfectly for this style. Also, I use other amps like the Vibro-King, the '65 Super Reverb (a real beast; try it with a fuzz in front if you're inclined to Davie Allan's style), and the American Vintage D (the Dual Showman), "rigged" as a Single Showman (EQ: American Tube Clean 1; Amp Model: 50w 6L6 + '64 Vibroverb cab).
Reverb: When I'm using the Reverb tank, I hardly use the onboard reverb (only 1-2, no more than that). I think you might sound so "drippy" if the amp's reverb is above 2 while the Reverb tank is on.
Compression: For me it always has to be low, very low.
Tape Echo: Classic slapback, more or less (115 ms to 250 ms; 1-2 repeats. My range is 135-165ms).
And the most essential thing: a single coil guitar! And some of technique would not come bad either
My advice: just experience and innovate, pal! Try other amps, pedals, settings... Surf rock has evolved a lot since the 60s
I hope I've helped. Surf on!