I found the two jobs hardly interrelated...a lot of people seem to think that having a PPL or a CPL automatically means they will be super ATCs, this is sadly not correct at all.
Spatial Orientation, Attention to detail, ability to multitask, ability to see a job through to completion no matter what is happening around you....all of these and a few more are ESSENTIAL tools/abilities for a prospective ATC. How you talk to the mike is really not, anybody can do that with enough practice.
You also need the ability to think in 3D....This is why people from all walks of life need to be screened for suitability as an ATC and not everyone can do the job, be it a professor in physics, a CPL Pilot, etc.
As for practice....I suggest you start playing chess....yes, chess, the ancient game, it will allow you to practice thinking in 3D, planning ahead, etc.
As for saving for a PPL while doing ATC, by all means, but you will probably find that at the end of your days you will be very tired and further studies will not happen immediately, at least not until you consolidate your ATC career.
Just remember, ATC is not a job, it IS a career, and not everyone can do it....you can front up to a flying school and make your way to CPL....but unless you have certain abilities, no matter how many courses you take, how much you pay and what you do, you will not succeed as an ATC.