Unlike other advices here I would recommend you to stick to the tool you are used to. Switching to git requires some solid background in SCM. It is more powerful, but also has a higher learning curve.
I would rather advice you to use an extra branch for the core that is pulled into the branches that use them means svn:externals
.
For help have a look at the documentation here. This way you'll save yourself the tedious work of synchronizing the core for each branch. Even if you need one of your branch to stick to a specific revision of the core you can do it. The link does not even need to be in the same physical repository, what makes it a really flexible tool.
But make sure you use the 1.6 version for the client and server. I experienced some trouble with other versions as the format for the links appears to have been modified and extended.