Lower Level Outfield sections are the best options for catching a home run ball at Petco Park. Head to even numbered sections 126-134 in left field just after gates open and you might be able to grab one during batting practice.
The left field side has a number of other advantages, including being right next to the bullpens near Section 134, and good overhead coverage and protection from the sun in rows 6 and higher. The one downfall however is the near impossible views of the main videoboard.
If you can handle the sun on the right field side (also known as the Right Field Lower Box and Right Field Lower Reserved) these seats will be very close to the many fun amenities located in the right field corner which include the USS Midway Museum, Fan Photos, Power Alley, Batting Cage, and Pitching Cage.