Logic Pro 9 is the best version I have tested. I have been using it since it came out and occasionally still use Locic 7 with older material. I run OS 10.5.8 as this is the last OS that will support drivers for my audio interface, (M Audio Profire 2626).It will support OS 10.9 and 10 but I hate both as they have proved unstable with my configuration.
Upgrading OS's is dependant on Drivers for your audio interface. Check if drivers are available and if the OS is compatible with LP 9.
LP 9 and 10.8.5 has been the most stable combination yet so you should be good to go with 10. 7 or 10.8.
If you do install 10.7 or 10.8, be sure to install Rosetta from the Snow Leopard Install Disc as this will enable you to use older software.
Of course if you were smart, you will have partitioned you Hard Drive into several partitions so that you can install several Operating Systems to compliment your software. I have four so that I can toggle between them and test for software suitability.