Fresh Market Inc., a gourmet food retailer that emphasizes quality perishables in compact grocery stores, has filed plans to raise up to $345 million in its first public stock offering. The Greensboro, N.C., company operates two stores in the Tampa Bay area and hopes to open a third under construction in St. Petersburg by the end of 2010. Its stores generate two thirds of their business from deli meats, seafood, produce and baked goods. The family of founders Ray and Beverly Berry hope to sell much of their interest in the privately held chain that has 95 stores in 19 states, but retain control. In 2009, the chain earned $49 million on $862 million in sales, up from net income of $32 million on sales of $798 million the previous year.