That memory was tested and approved by MSI as it is on the list: https://www.msi.com/Motherboard/support/H81M-P33#support-mem-0 CMZ16GX3M2A1600C10 Yes. Shut down the system completely. Handle with care. You should have no problems Any of these should work https://pcpartpicker.com/products/memory/#xcx=0&s=301333,301600&Z=16384002&B=1200000000,1500000000&L=80,110&E=0&sort=price&t=11 Corsair vengence is good ram.
Yes, 2 8gb sticks of ram is no problem for this motherboard, but make sure that it is DDR3 SDRAM memory. Highest RAM speed that it can run is 1600 MHz. DDR4 ram will be the wrong voltage, so what you want is DDR3 1600 MHz.
looking at the specs, it should work.. however, we often Google or Yahoo-search for compatible RAM for a certain motherboard.. and the RAM that you are looking for seems compatible to your motherboard, according to https://www.pc-specs.com/mobo/MSI/MSI_H81M-P33/2300/Compatible_RAM , it appears that CMZ16GX3M2A1600C10 is compatible to H81M-P33 ..