Well, I saw a pair of compact cordless clippers on stateline tack that I really liked the small design, but they're only $13 so I'm kind of on the fence about whether to buy them myself. The one review they have is good though...albeit, they're small so I don't know if you'd want them for an entire body job. But for just small trim ups, they seem nice enough for the $$.
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.
Agree with mom2pride. The best all around clipper that has the capability to do body clips (if you're patient) is the Andis A-5. New they run $150 +; you might want to try to find one used. They are truly a lifetime purchase; take care of them and you'll never need to buy another pair. Occassional blade sharpening is about it.
You can certainly buy something cheaper, but you'll end up replacing them, so the lifetime cost would be higher.
Gong cordless adds cost, and frankly, usually means a reduction in power as well. The times I really want cordless are when I'm doing delicate face clipping on a horse that's bothered by the sound; then cordless is a real asset. There are some inexpensive ($50.) cordless trimmers that will handle faces and light ankle hair, there's one that has the option to convert to corded.
I think if you want to stay under your $100 budget; you're going to have to compromise on some of your other criteria.