Jisho

Disclaimer: I can not prove my assertion and it is a mere conjecture based on my biased experience as a japanese language learner living outside Japan i.e. not immersed in the language.

I think that 貯金する is way more commonly used than 貯める for twi reasons. The first one is that 貯金 comes in the vocabulary list of the みんなの日本語 book for beginners, whereas 貯める does not. As a beginner's textbook it is expected to contain daily, commonly used vocabulary. The second reason,that pretty much follows the same idea, is that if you look at the entries for 貯金 and for 貯める the first one is marked with the N3 and commond word tags whereas 貯める is not. In case of doubt, I would go with 貯金する.

So, my guess is: it is not so often used.

I'd rather say 買えるように貯金します。

https://tangorin.com/sentences?search=%E8%B2%AF%E3%82%81%E3%82%8B