General feedback from foreigners who have spent some time here is that living conditions are similar to those in Western Europe but the expenses are lower. An iGraduate survey carried out in fall 2011 shows that international students think the living cost in Estonia is much more satisfactory than elsewhere - it was 24% higher than the global average satisfaction with living costs.
Rough estimates about what it costs for one person to live in Tartu for a month:
Housing, including heating, electricity, water: 80-120€ for student dormitories, 250-400€ for rental apartments
Estimated pocket money, groceries, etc: 300-400€
Public transportation: 8€
Estonians don't have an unwritten rule about tipping, they tend to do it when the service is especially good. Bargaining is not a deep-rooted habit either.
Estonia has adopted the Euro, which makes it especially easy to accustom yourself to the prices and living costs. In most places, even kiosks and trains, you can pay with debit or credit cards. In order to make everyday shopping easier, perhaps you would consider an Estonian banking account. See the home pages of the main banks: Swedbank, SEB, Luminor and Danske Bank.