Cash out refi on rental property questions...

We are just getting started and right now we are hoping to land a duplex for WAY under market value.  We are hoping to pay cash of about $20k for a property that looks to have a market value of about $75k.  Part of the plan is to immediately refi the property to get as much cash out as possible, maybe up to $50k in order to replace the initial purchase and to gain some much needed seed capital to pursue other properties.

I have heard that this might not be too easy especially if we attempt this prior to having the property for a year.  I'm also curious about the financing requirements since this would be a refi on a non-primary residence?  Does this matter?  Would this count towards the limit of 10 conventional mortgages?  What other questions should I be asking of a bank of mortgage broker concerning this?

Thanks in advance for any feedback on this.