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I've got a website currently on shared hosting
If your website is running on shared hosting, then it will run miles ahead on a VPS without much effort.
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However 512MB RAM sounds very small.
A lean and mean Linux can happily run on 512MB of RAM with Apache, MySQL, PHP, etc. Just keep your Apache MaxClients low (around 10) and you shouldn't need to change much else.
A LAMP stack with 512MB of RAM can happily serve 10,000 pages/day if running a moderate Drupal/Wordpress website with sensible configurations.
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If all else fails, reboot...
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