I have bought several used Canons off craigslist for under $50 that I use for time-lapse photography.
That would be a cheap way to start and later you could get a more expensive camera if you wanted, but CHDK gives the lower-end Canons most of the features of a high-end camera.
A lot of mid range DSLRs have these features. You can get better lenses and other stuff as well for a camera vs video camera.
Also remember, no matter if the camera is undercranked or overcranked, you can always fool around with it in editing to manipulate what you’ve got.
You can get cheap but quite adequate remotes with intervalometers for many dslrs for $30 to $50 dollars from places like B&H or Adorama or Amazon.
For high speed slo-mo, something like the Casio EX-FH100 or EX-ZR100 may do the trick, although at the expense of resolution, 1000fps all but unusable, 224 x 160 at 420 fps not bad, as good as you got with analog tape, looks like 4x3 aspect ratio. Check out the reviews & samples on youtube.