As far as a tub goes or active resevoir ( as i like to refer) the dimensions are directly related to two things: growing area and number of plants. Also keep in mind the different stages of the plants life.

Typically you'd like to have AT LEAST 1sqft per plant (indica) and 3sqft (sativa) during its vegetative and flowering stages. That's my opinion. This is assuming an average without considering topping, lst, or ScrOG/SOG. Those things you have to accomadate for but in your case I wouldn't worry about it. If the plants are stationary and cannot be moved due to them being in a "bubbler" this a pretty good idea of how much space you want.

During the early stages of its life until the plant reaches it full height the plant will drink considerably less water while quickly drying your tank in it's later stages. You will find you will have to refill more often. A good final number for your plant (the the later part of its consumption) I would recommend 3 gals. per plant. I have gotten away with 6 plants in a 3 gallon container for the first 6 weeks of its life but unless you want to have to constantly refill and worry about nute concentration it's best to move them to 3 gals each for a full grown plant and anywhere from 1-3sqft+ spacing. Obviously, if your planning to grow more than 3-4 ft tall like a giant sativa then obviously more root space is needed.

When using a shallow tub, i ran a drip system until the roots were well in the water and then added a bubbler until i was comfortable enough to remove the top feed system. Should work with or without a shallow tub. Some people use sprayers but I find my way a bit easier for me.

I would go for a height of AT LEAST 12". Depending on the height of your cups because you dont want them sitting in the water. The taller the resevoir the better. And at that length and width I would do two full grown plants (1.5 sqft each) ... so at least a 12 gallon container (half full of water the other half to let your cups hang. I'm not saying you cant get away doing more plants in a sea of green or something like that but for just a basic grow that's my suggestion.

Remember to only feed nutrients at the beginning of the week and to add just ph'd water to keep the resevoir full. Id put a fill line somewhere on your system to know how much water you have... maybe build a smaller tank until your are ready to transplant them to there final homes. Remember it all really depends on how many plants and how you are prepared to grow them and what you feel comfortable with. Wanted to help and put in my 2cents.