AWS is very generous with their Lambda offering and for small projects, I doubt that you'll ever need to pay anythings (in free tier, it offers "1M free requests per month and 400,000 GB-seconds of compute time per month.") which in my guess is the best offering you could have.
On the top of all this, the best part is if you learn AWS then you can not only use it in your pet project but the same learnings can also be applied in your place of work (I doubt that they will use "VPS") which means you'll get promoted faster!
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Just to add a few more things: