I plan on starting up a new website and I want to keep the domain private so nobody tries to contact me. Is it still possible for people to get my information?
No, if the domain is private since the beginning. However I can reveal your identity comparing the advertsing on that site with others site that you own, for example.
If you apply a private whois for that name, yes that will slow me a little bit. But if i can figure out your other domains (for example from domain forum, your signature, etc), i can whois your other domains and i can get your information, except you protect all of your domains whois information or you do not reveal the others
I don't think anyone can get your information except the company where you register the domain . I used to register a domain with privacy service in Godaddy. The privacy service cost me $6.8 . We pay them, they are reliable to keep your information private .