Drupal 7 sites hogging my shared hosting account
Shared hosting is the bane of the internet -- I recommend not using shared hosting if at all possible stick with the VPS. Did you turn on Aggregation, and caching in your drupal install? Did you install APC and configure drupal to use it. If you use APC and are a read-heavy anonymous traffic site, then APC can be configured to store all your pages in an in-memory cache and you never even hit the DB.

Tweaking a website to maximize server usage is really really website specific. The low hanging fruit is stuff like Performance settings in Drupal, APC, maybe Nginx for a webserver, etc. Beyond that profile your site.

Alternatively as you mentioned you could cache to disk by using like Boost.