How easy it is for you to look for a job, work, and receive benefits in Estonia, depends on your nationality. As a member of the European Union, Estonia has arrangements that make it easier for citizens of other EU Member States, Norway, Iceland, Liechtenstein and Switzerland to come into the country for professional reasons. For others, different conditions apply.
If you hold a passport of another EU Member State, Norway, Iceland, Liechtenstein or Switzerland, you have full access to the Estonian labour market. This means you can freely come to Estonia to search for employment, make use of the Estonian job mediation services provided by Töötukassa, and settle here to work. No residence permit or work permit is required.
Anyone who legally resides in the country can receive social security benefits. Rights to benefits in Estonia are in essence based on the contributions paid into the system. If you have not paid contributions (because you did not work here), or have only a very minimal record, the benefits you can receive will reflect that.