try a muscle power if u can find any. For under 100$ u cant get racquets that differ much in speed/power/techniques etc - those things are only noticiable in high end racquets. The musclepower line in general is more offensive than the isometrics/carbonex'es. Only naming yonex line though, you can always look for other brands - carlton, wilson, black knight etc.
Racquets under 100$ would generally be designed for all-rounded players for any type of game, unlike the higher-end models which are designed for a specific game and playing style.
For Sotx, maybe you can also give W-4A a try. W-7 is not expensive, but the price of W-4A is even lower.
Have a look for a used Armortec 700 in good condition. This is the archetypical singles racket - tons of head weight and pretty stiff. The '07 version is a lot more durable than the previous one, so getting a second hand one isn't as much of an issue.
I think that the durability would be relative, as I don't think the new model is any stonger. The usual cost of an AT-700 is about $180+, so I doubt, even with depreciated value, that it'd be worth or sold for less than $120.
