I would instead leave all the power source and general control system in the sub, and simply use a wire bundle to power low voltage relays in the sub. Using cascading relays with some kind of resistor would give you 2 or 3 power level. Using 2 rotary switches with 4 positions uses 8 wires (live + 3 power levels each). Add an other 8 wires to activate “features” (lights, gripper, buoy release, ect). Regular RS232 wire can be bought cheap and in good lenghts. You might want to check a fan switch from a scrapped car heating controls for power level controler.
Put the relay panel into a sealed box, same thing with the battery. Water will get into your sub the first 5 or 6 trials for sure. Water pressure builds with deepness, trials in a pool wont prove that your machine will be sealed for 10 or 20 meters deep. Getting everything sealed tight will be your biggest challenge.
Using highly absorbent baby diapers might help keep the flow under control 
Silicon sealant will become your friend! Use liberally!
Subs are relatively slow to react, so you dont need very precise speed control. Look at the old sub movies: they got 1/4, 1/2, 3/4 and full power on the BIG things. Your small machine wont need more.
Using a wire bundle will give you more distance to control your machine, and only a small control panel to handle the sub (put it into those aluminum case, looks super professional!). For the camera, using a regular CCTV camera and some TV speaker wire (gotta check the lenght first) should give you visual. It displays on a regular TV, no need for a PC uplink unless you want recorded telemetry, saves money and time. The video signal also records on a regular VCR, and other cheap way to go.
If you dont have a real diver with you, and even if you do, use a real metallic wire to tie your ship to the surface, dont rely on the electric connection for that. cloths line is cheap and resistant enough for that. Use plastic ties to join the safety line and the electric connection bundle, and leave some slack on the electrics, so the real pull will be applyed to the safety only. Pulling on the electric can break wires inside the bundle, lot of fun to troubleshoot!
Do not forget to heat or circulate air on the clear dome tru which the camera looks, cause it will get condensation quite fast. You might also want to put a small ball compass in the camera’s field of view. If you use a sealed and separate module for the camera, try using desiccant (sp?) bags in it to absorb moisture. You can later on dry those small pouch in the oven or direct sun light and reuse them afterward. Some even turn pink when “full” of moisture.
For power source, try to avoid non sealed batteries: they might leak acid if the get upside down, that might ruin your work. Stick to sealed gel-cells. Use weight to lower the center of gravity and to make sure the sub will stay verticaly aligned.
If you really want to use a surface power source (say, very very long underwater duration), send it separately to the sub, tied to the rest of the cable bundle. That way, you dont need to care about the gauge of the wire, big for the motor, small for other functions. Always control your features via relays or such. Use fuses to avoid burning a motor while underwater.
Later, do trials with various propellers. You will be surprised of the results. You will understand why the US Navy pumped so much moneys in into R&D about those!
Better forget about using USB for anything. As a user already pointed out, 16 feets is the max official lenght. Using USB exender is a bit expansive, but if you like it, that’s a solution.
If you need computerized control and feedback, you will need to drop to RS232 or RS485. At 9600 bauds, you can have more than 2000 feets of cable! But you will need a computer down in the sub. Might be a good time to check for PICs and other cheap micro processor. Using relays will payoff at that point, cause those processor can not switch large current. You might also go the motor controller way, PICs also support those.
My final advice is : dont aim too high for start. Stick to the basics, make it work, and have fun with it. Later on, you will be able to improve, add widgets and stuff.