For a beginner at surf I would recommend starting with the Chantays' first album. Most of the songs on there are great and they are all relatively simple.
Stereo versions of any old surf tunes are better than mono for learning bass, as back in the early 1960s producers were more apt to pan different elements more extremely... so it's easier to pick out the individual instruments, including the bass part, in the mix.
Although some surf and surf/adjacent instrumental rock had simple bass lines and simple blues based songs structures, it would be wrong to think that most of surf music is like that. There were a lot of different influences pulled into the genre (which began before it became associated with/named after surf culture), including western/cowboy music, jazz, spanish/latin music, middle eastern music, eastern european music, etc. A lot of it was also shaped by the sound of the newest musical technology of that time (the guitars, amps, and effects).
The bass guitar would have almost exclusively been strung with flatwounds, and the recordings of that time didn't have gobs of low end in the mix, just enough so that you could feel the pulse of the drums and be able to discern the bass guitar distinctly from the other regular guitars. Often the bass would be playing in or near the same note range of the other guitars, but the meatier tone of the bass made it discernible, and it was often panned more to one side in stereo mixes which helped too. On many of the mono mixes it's really hard to pick out the bass line for the purpose of learning to play it. Occasionally you'll find a tune like the Bel Airs' "Mr. Moto" which didn't even have bass, and that can be fun to write your own bass part for. And then there's a tune like the Lively Ones' "Surf Rider", where the bass sounds like a bass VI being played more like a rhythm guitar (kind of like the Beatles' "Back in the USSR") so it's super hard to figure out, but the Ventures original version of the tune (called "Spudnik") has a distinct melodic bass line that's much easier to discern. And then there's the Centurians' "Bullwinkle Part 2" which you'd need to tune your E string down to D in order to even hope to play properly, although the bass sound on the recording sounds like they probably recorded the bass part much higher pitchwise and faster and then slowed the tape down, as even some of the higher notes sound like they contain harmonic content that can't be produced on a regular bass tuned down to D.
Playing-wise you'll have to learn muting technique to get the right kind of decay for the notes, and I'd recommend getting pressed felt picks (the D'addario ukulele felt picks with the holes in them are my fave) for the songs where you want more precise attack than fingerstyle, but a more gentle attack than a regular pick would give.