There isn't really a product that works with laptops to give them an external GPU yet at a reasonable price. The only thing that comes to mind is the Razer Core (www.razerzone.com/store/razer-core) but it is $500 just for the unit itself. You then still have to buy a GPU to put in it! And on top of all of that it isn't even fully supported except on their specific laptops.
As far as building a new computer, I always recommend taking a look at Logical Increments (http
/www.logicalincrements.com/) to get a parts list for your budget so that not any single component you pick out is bottle necked by any other. I think building a computer would be better if you are looking to go into gaming since your price per frame in game is going to be far lower this way.
Good luck!