How and where do I simply file for a state trademark?
Should I do a service mark instead?
I am trying to file a business name and a slogan, so I'm expecting to do two separate filings. I am in California.
I am by no means an expert on this but I have also been researching the subject. I believe that you would file with the US federal government and not the state. Here is a site for it: http://www.uspto.gov/
The important thing with trademarks is not only registering them but first making sure that there isn't anything trademarked or in use that is similar enough and in your field because even if you successfully register your trademark someone else can come and challenge you can win if its too similar to their pre-existing one.
LegalZoom.com also has searches and ways to do it online.