One of the Jays biggest contracts under Atkins - George Springer right now - doesn't look that good.
BJ Ryan was one of the best relievers in baseball at the time and had an awesome 2006 season. Sucks he got hurt. Came back in 2008 though not as awesome as he was in 2006 but still was solid. Not the best contract handed out, though if it was Ross Atkins who handed out that contract, I bet many members of his cult around here would say it's just bad luck.
AJ Burnett contract was great. Sucks he had the opt-out after 2008, but that turned out to be a great big contract signing.
I don't think JPR really had any other big contracts other than signing Vernon Wells to that big contract extension after his 2006 season. Wasn't the best and Wells had some disastrous seasons but that was market value for top players at the time. Frank Thomas was decent in his first season here, but was terrible afterwards. Atkins gave Morales a 3-year-contract so there haha. Corey Koskie signing was bad but he still put up a 1.7 WAR season and the Jays were able to move him to Milwaukee the following offseason.
As well at the time, Toronto wasn't a favourable spot for baseball players, so yes you would have to overpay by money and years to lure top FA's. Which is why they went 5 years with Burnett and Ryan in the 2005/2006 offseason or else the Jays likely don't sign either.
Off the top of my head, JPR made some swift trades during his tenure. For example, Glaus and Overbay in the 2005/2006 offseason. Traded Bobby Kielty for Ted Lilly after the 2003 season. Traded for Justin Speier after the 2003 season as well and was a solid late-inning reliever here for years. Traded Billy Koch for Eric Hinske. Traded Adam Peterson for Shea Hillenbrand who then was flipped for Jeremy Accardo. Traded Glaus after for Scott Rolen and then Rolen for EE haha. The one trade that came to bite them was trading Jayson Werth for Jason Frasor. As well early in his tenure traded away Paul Quantrill and Cesar Izturis for peanuts. Trying to think of some other moves.