If you are just hosted with a hosting provider you will be fine, they take care of security issues, my direction is I have a dedicated server and am responsible for my own operating system/ software installation and updates. I employed people in the past that were f**kwits. 
A dedicated server is only necessary when:
1. You have a lot of sites and it becomes economically unviable to pay $20+$20 etc per site, per month on a shared hosting service. It becomes cheaper to have your own server.
2. High traffic. On a shared service your bandwidth and site speed is determined by the amount of users also using the service.
There are probably a shitload of other reasons but my brain is fried from 12 hours of copy pasting old stuff into new.