I've been a longtime kayak fisherman and now I'm looking to purchase my first boat. I'm on a budget...I'm looking for something under $3000.

I'm leaning towards a used 14-15' flat bottom jon boat but I'll consider other options.

Here is what I want to be able to do in order of importance.

#1) Go duck hunting on the Brazos and other nearby rivers.

#2) Lake fishing

#3) Bay fishing/possibly duck hunting near the coast. (What considerations should I consider for saltwater?)

#4) Bowfishing

My wife would prefer something we could ski behind but I'm not sure a ski/fish boat would offer the versatility and shallow water handling that I can get with a jon boat.

Any advice and opinions are appreciated.

I think most importantly, do not get a freshwater boat with the intention to use it in the saltwater. I don't see that being too good in the long run.

Saltwater boat will have a galvanized or aluminum trailer, painted steel is quick death.
Saltwater boat will not have carpet, and all/any wiring will be sealed and secured, NO open butt connectors anywhere.

Flatbottom will go fairly shallow.
Tunnel hull will go much shallower.
Jet will run extremely shallow.
Airboats don't need water.

Each has it's own merits and negatives, you need to figure out what you really mean by shallow.

Fairly shallow is probably shallow enough. What about motor considerations for some saltwater action?

Is a flatbottom okay for the bays or do I need a V-hull?

Depends on what bay you want to fish. What works in Galveston would be a complete waste of time at Mansfield.
I run a jet on my scooter and have no problem running two inches of water. Why? So we can run the back lakes without worry. A tunnel can usually run four or five and no tunnel takes a foot. Which might not seem a big deal until you start trying to navigate and find out it is.

Every boat is a compromise. What makes them good in shallow makes it bad in deep. Why I ask how shallow do you want to go?