The Celtics’ two rumored desires coming into the NBA draft were a big man or backup point guard. They came away with the former last night after selecting Gonzaga center Kelly Olynyk with the 13th pick in the first round. Olynyk averaged 17.8 points and 7.3 rebounds a game for one of the top seeds in the NCAA tournament last season. The 22-year-old will likely compete for a job in a Celtics frontcourt that was depleted last season and will be in flux before the new one starts with the reported deal of Kevin Garnett and Paul Pierce to the Brooklyn Nets, signifying the beginning of the rebuild in Boston. “We watched him play a lot this year,” Celtics president of basketball operations Danny Ainge said last night at team draft headquarters. “He’s a 7-footer who can shoot, pass, think. Has a great feel for the game. We think he is a very good complementary player. . . . He’s a real good character kid.” The Celtics entered the night with only one pick — the 16th — but moved up in a trade with Dallas once Oklahoma City took 7-footer Steven Adams off the board at No. 12. The Celtics traded the rights to the 16th pick and two 2014 second-round picks to the Mavericks for the rights to Olynyk. The C’s then drafted Brazilian center Lucas Nogueira in the 16th spot for Dallas. “We weren’t real confident that Kelly would be there at 16,” said Ainge. “There were some other guys who were there at 16, but Kelly is a guy that, again, that he complements (Rajon) Rondo and Avery (Bradley) and Jeff (Green. He’s just a real complementary player.”