My PC was about £850 ($1.1k) and although I'm thinking about getting more RAM, it will work GTAV and LSPDFR (+Plugins,cars ect) perfectly, and if you have a higher budget I would get more RAM/more GPU memory. As Break said, if you buy from a company like Alienware, they'll charge extra for the logo.
Heres my specs you can use as a reference:
https://gyazo.com/f6c05b2cb0b624ee299de1fd1b8dee06