ive been building hobby grade cars for about 18 years and race rc every friday night so i think i can help you out. first off the lipo batteries are great but require a lipo charger, a good lipo charger can be had for aroud 40 bucks. if you run lipos you will need to have a speed control with a lipo cut off, if you dont have a lipo cut off it very easy to ruin your lipo packs. once you drain a 7.4v lipo past 6.6v its junk and is totally unsafe to charge.
the green motor you have is a brushless motor and requires a brushless speed control. the other electronics you showed a brushed and would work just fine, keep in mind that brushed esc doesnt have a lipo cut off. if you go to hobbyking or hobbypartz you can find a cheap esc that will run that brushless motor and have a lipo cut off in it.
i did a hooby grade conversion on my eliminator and used an axial ae1 speed control in it. it was the only esc i could find that would allow me to run the stock tyco battery packs. i used the axial esc with the stock tyco motor and it was a huge difference, the truck will wheel stand in high gear from a dead stop. if you need more info just ask.
