I have no idea why people are afraid to answer this question.
Of COURSE, the racquets you can buy for $20 at Wal-Mart have a definite performance ceiling.
There are racquets available through this site which can be (and often have been) used right up through the top ranks of the professional levels -- and which are available for less than $75. Usually because they are no longer "current fashion."
As long as you don't need to use the model that's painted exactly like the one your favorite player uses, you can get a professional-caliber stick without dishing out 200 bones.
A few quick examples of racquets you can use just fine at recreational level, but can also "grow into":
The LM Radicals -- currently selling through TW for about $75. The OS was considered a power baseliner's dream racquet only a few years ago. You could still take it out and pound with the best in the game today, if you had the game to back it up. The MP size is a very versatile stick, and would be good for anyone up to and beyond college level who played all-court, or doubles.
The Prince NXG's are currently selling at around $70 on this site -- albeit mostly in smaller grip sizes. People decided they weren't an improvement over the POG, but they're solid racquets, available in a variety of styles. All pro-tennis worthy.
The Prince TT Warrior. Got the seal of approval from multi-slam winner and world #1 Pat Rafter less than a decade ago. Awesome stick, even by today's standards, particularly if you enjoy doubles or net-crashing singles. Sells here for $70.
The Dunlop M-Fils. The 200 series was considered their "pro level" racquet. The 300 series a little more "recreation friendly," but still with plenty of high-level devotees. Either of these racquets will allow you to ascend as high as your athletic ability and dedication allow. And both can be had for $70. The drawback? They're ####ing hideous. They look like candy canes.
Any or all of those should meet your price/performance guidelines. The lowest-price bats TW sells that will be fine for the recreational beater (because truly, at that level, it DOESN'T matter what you use), but will also be fine if you progress upward on the tennis ladder...no matter how far you ascend.