The VPS provider has your payment records and connection logs with your real IP. Since you and friends or family are presumably the only ones using it, your identity would be really easy to unveil.
That's more like just changing your IP once, though, not putting your traffic along with hundreds(+) of others through one IP. If you build it yourself, then you have a lesser degree of anonymity.
The easiest way to do it is by leveraging the existent communities.
Search for places where your potential customers hang out and start to help people, ask for feedback.
I did it for all my last products, that's clearly the easiest way to start getting your first users.
As in "you have an audience for your content already". This is more relevant on other platforms than reddit is, although you can get famous as a 'reddit-specific' user I think it's more difficult.