I can spend $15-$20 and I am looking for a good yoyo. What could I get
Responsive or Unresponsive? ??? ???
First decide if you want responsive or unresponsive. Based on price range though, try something from Yoyofactory or Yoyojam to start.
Can’t decide? Lyn Fury. If you want it responsive, yank the rings and use silicone or put in YYJ silicone response pads.
YYF ONE, 2011 or preferably 2012 version. Get the 2-bearing option.
Unresponsive: Adegle PSG or Asteroid.
YYF Starbrite
5A as a complete set: YYJ Pinnacle.
Inexpensive? Yes. Cheap? If by price, then yes. If by quality, then NO as all are good quality yoyos.
Enjoy.
Lyn fury for sure. Starts responsive and is easily modded.
Um YYF:ONE,Whip,Starbrite,One Star (though its only available through BAC so go BST)
YYJ:any of their cheap plastic line speedmaker,lynfury,etc however lyn fury is probably the best choice
Adegle:PSG and Asteroid
For now thats all i can think of 
I love my Lyn Fury. I use it with one O-ring out and with a CTbearing and it is extremely smooth.
For $10, the Shinwoo Phantom is really good, and comes unresponsive.
The Lynn Fury would be my pick if you want to start responsive then move into unresponsive with the same yoyo.
If you are wanting a yoyo that you can easily mod later, get an FHZ.
If you are wanting to try both looping and string tricks, get a couple of Pro Zs.