First off, I have not done a data migration like this myself, so I am not familiar with Mavericks specifics (I hope others will add helpful info). That said, data migration from Macs running older OSes to Macs running the current OS is (and has been) a fairly straightforward procedure, as described
here and in the links listed.
For data migration, there is no need to update your source Mac's OS to a version newer than what you got (Snow Leopard). If you want to upgrade the OS to Mavericks anyway (something you said you don't), you need Snow Leopard or higher as a starting point. Either way, you're all set to go!