I know that some DC motors produce a lot of torque but only actually move at a very slow rate, while others do the exact opposite. I know that I need some sort of balance between torque and the RPM's of the motor for use in a underwater thruster, but I am not sure what I should favor more, torque or RPM's? Also, it would be great if someone could suggest a motor at or below the $300 range for a UROV.
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The engine's ideal torque and RPM characteristics are dependent on what propeller you use. In general, if you know about how large of a propeller you want (relative to the size of your vehicle), you should be able to work backwards from there to find the ideal motor torque/RPM to support that. There will be a few options, based on possible variations on the number of blades, attack angle, etc of the propeller.
OpenProp may help you if you're approaching it from a very theoretical angle.
This question about upgrading motors on the Sea Perch ROV also has some insight that you might find relevant.
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$\begingroup$ Also, most hobbyists just use bilge pump motors. $\endgroup$– IanCommented Apr 7, 2015 at 12:58