Unfortunately unless you buy used, you are not likely going to find a clipper that will do faces, bridle path, and body for 100$. Even some used ones will cost you atleast 100$, and sometimes you're not guarenteed the actual quality of the clipper. I have not used a cordless clipper, ever, on a body clip...I have one that I use for legs, bridle path, etc...but wouldn't ever try using it to clip an entire body with.
If you want a clipper that won't cost you an arm and a leg, but has enough power, and is fairly compact I would go to petedge.com, and look through their clippers...they have pretty much any brand you could 'ask for'; I groom dogs full time, and have never used anything but Andis, and I have several of their models including the AGC cordless. I have clippers that are over 10 years old, and none of my current clippers are under 2 years old, so they last if you take care of them...same with blades; I haven't bought a blade in over 2 years, and have had some since I started grooming way back when.
"The ideal horseman has the courage of a lion, the patience of a saint, and the hands of a woman..."