I own several Aqua Vu products, primarily for ice fishing - a reconditioned Aqua Vu mini is handheld, mobile and can be had for under $200. Sounds like a good fit for what you want to do, but to manage your expectations clarity will impact your field of view significantly.
That being said, the next larger camera I purchase will be a Marcum - fewer issues than the Aqua Vu.
My handheld cams are a lot of fun to use and educational. I use them in cages to verify condition of fish without having to use nets and stress them, can verify volume of uneaten food on bottom of cage to modify my programs, and can verify species of vegetation anywhere around the pond, etc. My water clarity ranges anywhere from 40-100", so cams work very well for me. Again, your experience will be different with the reduced clarity.
Hope some of this is helpful.