If you are planning to use Piwik, it's a very good idea to choose hosting, or server environment that will let you scale as needed. Piwik is great out of the box for low traffic sites, but once you start getting any amount of traffic and get into monthly and yearly archiving, you're going to wish you had planned for scalability in the early implementation phase.
Our current Piwik database is 38GB after about 7 months, and sits on it's own server, using Nginx, caching, 8GB of RAM, SSD Drives (RAID 10) and a quadcore processor. It works extremely well, but you just have to make sure you have sufficient hosting environment -- or a scalable option -- as your sites and traffic go. Certainly you don't need anything expensive to start with a lower traffic site or sites.
Piwik has several helpful guides for implementation on higher traffic sites:
How to configure Piwik for speed - Analytics Platform - Piwik
That said, I quite like Piwik and find it very effective -- more especially since the stats are stored on your own server versus at a 3rd party (like Google Analytics).