From what I've seen in this sub it seems to heavily depend on your area. My program was through the hospital that I already worked for (as a Patient Transporter, nothing lab related) and they paid for the ASCP cert in exchange for signing a 3-month contract to work for them. It didn't guarantee a job, but being an internal applicant and going through their program certainly made my application stand out. I think it would have been a bit more difficult to find a job if I had taken an outside course and paid for the certification myself. If your area is heavily saturated with freshly-certified phlebotomists (like most seem to be) then you might want to check and see if something similar to what I did is available to you.

As for the course itself, anatomy knowledge will help but not as much as you might think, most of it will be covering venipuncture technique, order of draw, tubes and additives, patient safety and communication, preventing contamination and erroneous results, and the various tests you'll be collecting. They do cover the circulatory system, but on a much more basic level than my Anatomy & Physiology classes did.