Organize your move to Estonia

What would you bring and what would you leave behind?

Bring: Money, Passport, International useable credit/debit card, Certified copy of university diploma supported by the Hague convention. Certified copy of university transcripts, Original copy of diploma. (need these items to get a job or go to college) Pair of very good snow boots (DC makes some), Good jacket. bringing medical records isn't a bad idea either if needing a doctor.
Leave behind: Everything you can't carry...

Is it a good idea to bring furniture or domestic appliances?

Bring what you need, and if on a budget buy everything you need for your home from a second hand store. If you get an apartment anyway... a number of them come furnished.

Any foodstuffs that are banned in Estonia?

Not really sure about this, but be sure to look closely.

Is it better to bring a car or to buy one once settled in Estonia?

If you live in Europe and own a car and are moving here, bring it. Cars are better quality from other parts of Europe, but in Estonia, cars are certainly cheaper.

Any advice for the ones who are moving to Estonia?

Simple: Good Luck!