How easy to integrate wordpress into your site?

Hi, I've got a blog:

https://greyaliengames.wordpress.com/

but it's on the wordpress site and I'd prefer it to be on www.greyaliengames.com for speed and so I can tweak it more etc. Anyone know how easy this is for a relative web novice like me?

Also I heard that it's worth getting a separate domain for the blog so that you can link blog to site and vice versa for better google rank...any thoughts on this?

thanks in advance for any advice, links etc...