I'm going to attempt something I haven't yet done however i am presuming it's not that complicated to complete.

I have to pull content from another MySQL database onto a WordPress page. Another database will be employed to track high lots of a game title and I have to have the ability to pull extremely high scores to the site.

Could someone please let me know the way i would build a storage shed?

Thanks!

Produce a wordpress widget that connects with this particular 'high scores' database, pulls data needed and shows them.

If database is on other server than your wordpress installation it might be difficult for connecting into it directly. If that's the case, produce a openly accessible script that pulls the information and results them as ie. JSON on a single server where 'high scores' DB. Then produce a wordpress widget that reads that data (using PHP or javascript) and shows them.