In most states, all three of those represent the same thing. LPCs/LMHCs/LCSWs typically work more with individuals. LMFTs work more with families and couples. Rehabilitation Counselors are nationally certified and tend to focus more on working iwth people with disabilities and addictions.
LCSWs often get paid a little more (mainly for political reasons).
A Counseling Psychologist is the next rung up as far as compensation and recognition in court as an expert.
What type of setting are you wanting to work in? It sounds like you may want to look into being a counselor with a specialty in Employee Assistance. That is the new "buzz" word www.eapassn.org/i4a/pages/index.cfm?pageid=332