Like Finland and Germany, Estonia is in the euro zone. A few shops will let you pay in dollars or pounds, but the exchange rate is rarely good.
An exchange office is inside the terminal. There are more ATMs and exchange bureaus all over town.
Ordinary things are not as cheap as in St Petersburg but the range of high-quality items is better. Prices are sometimes far cheaper than in Finland but the range is not so great.
Serious antiques can't be exported but there's plenty of junk from the Soviet era on sale. From 1940 to 1988 Estonia was a "socialist republic" of the USSR.
In Tallinn, the farther you travel from the town centre, the lower price and quality get. Luxury goods are available in all Baltic cities, of course, at luxury prices.