Welcome bparker! Like doug said, it will be hard to find a running good motor at that price..You might end up buying one that says "running good" and bolt it on to find out it's not so good.
What i do know, is the Honda ATC 200S motor will bolt right on, alot of people on here have done it. The only difference is that the 200S is a Semi-Auto Tranny, with no clutch.
When putting one on the 200x it's called turning it into a "auto-x". The 200s shares alot of things with the X, both 192CC engines, the X may have more torque though.
Like cody said, try and find a beat up POS that still runs, probably your best bet. Find one that was rolled has a bent frame or something around those lines that the motor is still good.
Good luck with your project.
~~ATC's Currently Owned~~
1983 Honda 200x - Main ATC
1985 Honda 200x - Parts Bike
~~ATC's Previously Owned~~
1983 Honda 250R
1984 Honda 200X
1979 Honda 110
1983 Honda 125M
1984 Honda 200
1983 Kawasaki klt 200a
1986 Honda 200s
~~Other Toys Owned~~
2012 Pro R 800
1993 Polaris Indy 500
2004 Yamaha 125
1990 Thunder Kart - 250CC
2001 Yamaha Blaster - 240kit, aftermarket exhaust, power reeds