If you want to do some good 3D with the plane you will need an engine that can turn a 13x6 @ 10,000 RPM minimum. There is a lot of difference between a 5 lbs and 6 lbs plane. I think the Groovy will come out at about 6 lbs max, WM is pretty accurate when it comes to the plane's weight.

For 100-120 dollars you do not have 4C engines as an option. A TT46, OS46AX will not be an option for good 3D as they will not be able to handle a 13x6 prop and is not near your budget. You may get away with an MVVS49 or the ST G51 turning an APC 12x4, both engines are nearer to your budget. The MVVS49 is reliable but you may have some problems trying to get an extension for the high speed needle. The ST51 is a very decent engine too.