300 ppi is probably more than is required for a large poster, but I've rendered larger than 7200 pixels in PP2010 with no problems, albeit with long render times.

I'd think in terms of 150 ppi - 200 ppi for a poster (3600x3600 - 4800x4800) but as suggested, confer with your printer, as "300dpi" tends to get specified - because it's the easy answer - when it's really not needed.

A cheat would be to render at 200 ppi, then interpolate in Photoshop to 300 ppi and apply some very subtle sharpening (smart sharpen rather than USM). It will be very difficult to spot the difference between this and a genuine 300 ppi render unless your nose is almost touching the poster. (More here).

Large renders will max out your RAM and CPU usage and make your PC unresponsive, which can look like it's just doing nothing or has hung. I'd use PP2010's queue and leave it to run overnight. 

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Windows 10 x64 Pro - Intel Xeon E5450 @ 3.00GHz (x2)

PoserPro 11 - Units: Metres

Adobe CC 2017