BRYAN, the answer is.... it depends
the first thing is the dimensions of your tank, without them there is no way to answer. Your tank size will tell whether the overflow is appropriately sized to provide efficient skimming surface area. Coast to coast overflows offer the most skimming surface area with lengthwise being the absolute best. overflows sized less than full width leave some "dead" spots. More flow will help move some of this however with C2C overflows it is a non issue.
As for fitting a bean animal, you would need to draw it out and see if you have sufficient space for the elbows, bulkheads, etc the the space of your overflow. Note however bean animals are not designed for full depth (traditional top to bottom of tank) overflows. Some have made it work, others scubas myself have opted to remove the traditional overflow and build a new coast to coast in it place. You can find more detailed info on the bean animal thread or his webpage. All that being said, 3" front to back is probably too narrow to put the elbows in, grab an elbow and try it....although I believe the recommended min pipe size is 1.5"... if you have a small tank perhaps 1" will work.
The amount of water is determined by your optimum flow rate for your sized tank or your preference, a bean will work with slow to fast flow, that is some of the reason the needle / ball valve is needed. To determine your tanks optimum flow rate look for aquarium flow calculators.... it will depend on what you are putting in the tank and the tank size. From there you can deduct quite a bit using powerheads, so deduct your plans for those from the overall flow. Now your left with the flow of your return pump. I would allow for some flexibility in this as you may change add/remove powerheads, you may want to increase or decrease flow.....better to have a return pump that can accommodate all of that. Then there is head height.. how far up from the sump will the pump have to push the water? pump flow rates change with head height and are listed in the specs. There are pressure vs. non pressure rated pumps, most of us use non pressure rated pumps for returns, unless you have a lot of head height (pumping from basement up, etc). There are DC and AC pumps.. its a personal choice. There are variable speed pumps (usually DC pumps) again its a personal choice... neither of these options are wrong or right.
So as you can see it depends.... If your still confused then you should do more research on these topics. It can be quite involved but don't let it overwhelm you.. building a new system is a lot of fun. The design and planning are part of that.