Prior to SSDs becoming commonplace VPSes would murder any reasonably active forum, so I've been strictly running my own servers for years. Back then properly dividing out CPU time was also problematic for the most common VPS providers, which caused its own issues. VPSes can also end up with very weird issues still... I deal with VMWare professionally and sometimes you get some insane headscratchers.
A VPS these days is fine for most people, just make sure they are not running Virtuozzo, and make sure you are on an SSD.
Specifically, even if you want to start smaller, make sure your VPS can dedicate CPUs to you. If you outgrow shared hosting, you'll probably want two CPUS fairly quickly, and enough RAM to hold a significant fraction of your database.
Much further gets into how to monitor these things, but you'll want to learn how to distinguish between your CPU getting topped out and thrashing due to low RAM. Novels can and have been written about optimization, etc. I get a lot more out of my hardware than most people do.
