Here's what I've seen. First you’ll need a service provider (you can’t really avoid it) we tried grouhub,Manuel the guy was very kind. 500€ for the incorporation and he referred us to get the bank account . On the other hand, don’t incorporate too early. If you’re still validating, you’re just paying overhead for nothing(180€/month).
On initial capital: you can set it at €10k as it helps if you plan to structure/share ownership more seriously later, but plenty of people start smaller and adjust when needed.
You don't need a service provider other than a "contact person".
The actual minimal cost of getting e-residency is a one time €150 state fee (I guess you have to renew the physical card every 5 years, which is €150 again?). If you also want to incorporate an Estonian company (which you probably do in this context here), then the registration for this is a €265 one time state fee.
There are no other mandatory fees, except you have to find a "contact person" who's responsible for receiving official government communication on behalf of your company (don't worry, I have never gotten any physical communication from any gov agencies during my 10 years of having a company here so this "contact person" won't actually be doing anything and is just a formality). After a 3 minute google search, this service can be had for €7 / month.
If you don't want to file taxes yourself then you'd also need to hire a local accounting firm. That'll start from somewhere around €50/month for a micro-SaaS. If you really want to, you can file taxes yourself for free but.. your call if your time spent learning the Estonian tax code is worth the saved money..
