As far as the Google question, I'm fairly sure it won't effect your rankings at all. Most hosting you purchase have 25+ websites on one server. Google knows this, and knows it's a valid and well-accepted part of the industry, so I'm sure they focus on the domain rather than the IP of a website.
As long as you focus on normal
SEO, no duplicate content, etc. you should be perfectly fine.
Now, as to running your own server. It's a pain, for real. I will never run my own server again, unless I absolutely need it. Shared hosting is so much easier to work with.