Welcome back to rc.
What Futaba radio was this that you heard about? The Futaba 4gwd is the most economical if you don't mind it being 27am frequency.
The bruiser is a nice truck, but the main appeal is nostalgia for people who remember it back in the 80's. The high lift should work well for you.
There generally isn't such thing as crisp steering in mud.
Good mud tires would help the most in that respect.
The 3 speed in the high lift is the same trans as what's in Tamiya's semi trucks. It's made to be able to handle loads, so I don't think you'll have any problem with it.
For just the basics, you'll need 2 servos(1 for steering, 1 for shifting), radio system(radio and receiver), and esc(electronic speed control).
For tools, you'll need a couple different sizes of phillips(+) screw drives, side clippers(for removing the parts from the parts trees), and maybe a hobby knife(optional for trimming parts once removed from trees). Hex keys are included in the kit for the screws used.
Also, the High lift's body is injection molded plastic. In contrast to many cars and trucks that use lexan bodies, the body must be painted from the outside with plastic model paints.