You can use Unicount online company formation service to register an Estonian limited liability company (OÜ) with a single founder, shareholder and board member (being you).
Restrictions are related to the API service provided by Estonian Business Register to company formation agents such as Unicount. If you need to register a company with multiple shareholders and board members please follow the advice here.
The standard articles of association that are used with the fast company formation service foresee postponed share capital payment in an amount of 2500 - 25 000 euros. We recommend to stay with the minimum 2500 euros if you are not sure. You can see the standard articles and find our practical comments to the standard articles here.
You can deposit and register your share capital later on by following our manual here.