Absolutely D&D 5e is pretty good if you want a fantasy based system. But what exactly did you see for 20 bucks?
There is a starter set which has everything you need (except for a pencil) for a taste which is around $17.50 on Amazon.
The alternative to that is the D&D Player's Handbook and you may also want to add in the Dungeon Master's Guide.
For the PHB/DMG combo you will have to write your own adventures OR buy extra material (fan adventures are also available to download). You will also have to buy dice.
The big advantage of D&D 5e is that there is also lots of organised play.