I believe the m9a comes with thermal paste, let me know if it is no good.
Thermal paste should be fine, you could always buy arctic thermal paste for 6$ though. No need to get better cooling, the cpu doesn't run that hot. But you can never cool your hardware too much.
In the compatibiliy notes it says the following: The CRYORIG - M9a 48.4 CFM CPU Cooler may require a separately available mounting adapter to fit the Asus - STRIX B350-F GAMING ATX AM4 Motherboard.
Will this be an issue?
Yeah most older coolers will have this issue, but It is an easy fix. You just need to buy an AM4 bracket from the retailer who sells the cooler.
It seems to do this for all the coolers though.
http://www.cryorig.com/getam4.php its an AMD thing
goto the R1 / H5 / C1 / M9a diagram, when you get your cooler if the bracket matches the left, you are good. If it matches the right, you need to buy an AM4 bracket which is really cheap but its a problem you will see often. So you can't really get around it. If you want to get to building as fast as possible, I would order it just incase so you won't have to wait any longer.
Turns out that newer versions of the product already have am4 support so im all good, I've ordered my parts.
Thank you for all the help and support.