In Estonia there are two options for a limited liability company:
"AS" (in Estonian "aktsiaselts", can be treated as a public limited company)
"OÜ" (in Estonian "osaühing" or private limited company).
For a small company, it is recommended to use an "OÜ" for simplicity. Currently, there’s no special format for a single owner company. There are plans to introduce a new format for this purpose (called SUP) in the EU including Estonia, but it won’t happen within the next 1-2 years.
"FIE" is a sole proprietorship (full individual responsibility) which LeapIN does not recommend nor support.