To be clear, is it $25 + the string you provide? Or is it $25 total (string + labor)?
And how often do you restring a racquet?
In the end it will eventually be worth it, but how much you save (and how long it takes to recoup your costs) will depend on the answers to my questions above. Also, as
@RadicalEdward23 mentioned above, its a great way to make a few $s on the side. But beware: Stringing your own frames can take you down a rabbit hole all too quickly, and its extremely hard to climb out of it.
You quickly see how many strings there are. Polys (shaped, smooth, rough, twisted, etc), Multis, Synthetics, Natural Gut, Kevlar, Zyex, etc.. Then you consider blending them, adjusting tensions. Then you work in the different colors, and soon you have no idea what works for you. It can be extremely maddening, but also fun in a masochist kind of way...
So, in the end, yes, buy a machine. I'd recommend a drop-weight to start (there may be used ones on the 'bay). If after a few years you find you enjoy it and you're stringing regularly, maybe look into a crank.