Having a fat tire bike will give you better traction in corners and a smoother ride but in turn will be slower and cost more to fix flats and busted rims, I find myself breaking rims every 1-2k miles just from ridding but I'm pretty ruff on my bikes.
For a fat tire bike I would reccomend getting the Mongoose Terrex. Keep in mind most fat-bikes even with a shift kit will need mods because the shift kit might rub the rear tire.
I just used a Kent Glendale and put better breaks on it, off road Kevlar tires so I dont get flats every trip like I was. People talk a lot of smack about using walmart bikes but its not that bad if you replace the crap parts like breaks rims and tires etc other then that they provide some nice frames. I normally only replace the rear rim when I get their bikes.
Heres a pic of mine;
Keep in mind a fat tire bike will be very slow. Even putting a solid tube in my 26x1.95 rear wheel slowed my bike down to the point where I went out and spent the extra 50 dollars per tire on high quality tires.
The engine is very small and weight impacts them a lot, personally I would stick with a generic steel frame mountain bike with front suspension, if you really want a dirt bike buy one, but these will never be like dirt bikes. The lack of rear suspension really makes bikes with fat or regular tires a really rough ride when you add a motor to the equation, but still fun. You might be able to find a TTR 125 for 500 dollars if you look around enough.
Here's a video I found and enjoy a lot of just a old junkie mountain bike on a trail, they do well with just a regular bike. Love this! (Poor Mans Dirtbike)