Chris-
You'll have to pick the net out yourself based on your fishing types and where you decide to store it, but here are some ideas:
Some of the newer ones made up of soft machine woven netting are great for not harming catch and release sensitive fish, such as trout, but trebble hooks from lures really get tangled in them quickly and are hard to remove.
The simpler tied and knotted plastic multi-strand ones are easier to use in this respect. The size of the netting squares is another consideration. Bigger ones for bigger fish, but not so big that the smaller fish you'll net fall through the mesh. This type of netting is also much easier to repair than the fine woven type.
The longer the handle, the easier they are to use, but up to a point where they become akward due to the extra handle shaft in the way once the fish is really close to the boat.
Storage is another issue. The simplest place I've found to get the net readily available and yet out of the way of fishing rods, downriggers, and everthing else, is to mount the net vertically behind the hooked open cabin door. (Most folks have rod storage on the starboard side.) Some may choose to mount the net in the middle rear of the cockpit in front of the motor well, but it's much more in the way there, IMHO.
Take a piece of PVC pipe large enough to allow the handle of the net inside, and mount it down alongside the door hook. The length of the handle is also involved in this, as a handle that is too short will allow the net hoop to jam down in between the door and the cabin bulkhead. Too long a handle, on the otheer hand, will allow the net to spin in the wind. However, there are ways to make a short or really long handled one fit here, just requiring some more ingenuity and hardware, such as a bottom stop for a short one, and some friction lining in the storage tube for the longer one. Some higher quality nets also feature a sliding handle that stores up inside the net hoop to reduce their length for storage.
You can also mount the net on the roof laying it horizontally, but you'll have to add some form of keeper hardware to hold the handle. Moreover, if it's not really secure and you move the boat w/o tying it down good, you'll lose the net over the side going through the chop.
If you think you'll ever drop the net over the side accidentaly, you might take off the handle end cap and stuff the inside with styrofoam macaronni for some flotation to save the (net) day! A net would be hard to see or find if you were looking for it in confused seas, just like a lost spinnaker pole on a sailboat. I'd wrap the handle with a bright colored tape in an open spiral pattern so it could be seen easily.
Nets should be stored inside the cabin or some other similar place, as leaving them out in the sunlight and elements eventually breaks down the plastic fibers of the netting.
Almost all net frames and handles are made of aluminm or Al alloys. There may be some ultra light carbon fiber ones available, but they'd be disproportionately expensive, and the money could better spent elsewhere, such as a downrigger upgrade.
It might just also be that if the different types of fish you'll be catching are too dissimilar, you might in turn consider having two nets of different types instead of one universal one.
Others will have more ideas to share with you, I'm sure!
Good Luck Fishing!!!
Joe.