Yes and yes

I am applying for a job I found on Craigslist. It is not a "formal" job, per se, but is more formal than being a nanny (what I do now) or applying for a retail job, etc. The post asked for "work/character references" to be included. Do you guys think 2 work and 1 character reference would suffice? Is it okay that I'm not listing my current employers as a reference, as I do not want them knowing I am job hunting?

Thanks!