Just pulled out of Branson after 5 days on The lake - so here is probably more info than you want.....
There are 2 lakes to choose from - Tablerock is a big traditional lake with a rocky bottom so is relatively clear and beautiful. Lots of boat rental places and standard freshwater fishing for bass etc. tho we have never fished it so not much help on that. Great for waterskiing, tubing, wake boarding etc.
The other option is Taneycomo which is where we always stay. It is more like a wide river - The water for Taneycomo comes off the bottom of the Tablerock dam so it is cold year round. It is too cold for most people to ski etc. (although we have tried it a few times) and the Only fishing is for trout which they stock constantly. Since the water comes off the hydroelectric dam the flow fluctuates with the need for power. This time of year it may be almost still in the morning but the current quickly gets faster as they start opening more gates on the dam for Electricity. Late in the day it gets a little sporty trying to dock a big pontoon boat that handles like a pig. Lots of places to rent boats - anything from a small flat bottom to bass boats and Pontoons.
If you are wanting to get on the water and fish with little ones, Taneycomo is a great option. Rent a Pontoon so there is plenty of room to move around and less chance of anyone falling out.... The trout fishing is easy - before the current gets kicking you can anchor throw out several rods with powerbait floating up off the bottom. Once the current picks up you can drift. The boat rental places will tell you some good spots and there is a high likelyhood of enough action to keep everyone from getting bored. You won't catch any trophy's this way but can easily catch a meals worth of trout filets. Lots of wildlife on the lake too - geese and ducks (we saw lots of baby ducks) swimming everywhere, deer and marmots on the shore, and we saw several hawks and a couple eagles.
As far as where to stay on Taneycomo (no help on Tablerock) - if you want to stay on the water there are a bunch of 1950's style lodges and RV parks with cabins. They have docks where you can fish, pools, playgrounds, and most have their own boats to rent. Our favorites are Cooper Creek and Lilly's Landing, but there many more to choose from.
We avoid Branson proper at all costs - as mentioned above it is full of blue-hairs on bus tours going to all the hillbilly country music shows.
Lastly there is Silver Dollar City which is sort of an amusement park. Has standard amusement park rides plus a bunch of hillbilly craft exhibits. Worth a try if you want a day off the water with the kids.
Hope that helps.