Heroes of Battle is the place for the most updated siege rules, including a number of feats (Ballista Proficiency, Expert Siege Engineer, etc.). The relevant feats may be selected as fighter bonus feats, so that makes fighter a possibility here. Fighter is also good for getting crossbow feats—the rules do not specify that feats relating to crossbows apply to ballistae, despite being just an over-large crossbow, but if allowed, fighter is in a pretty good place to get them.
Dragon vol. 295 has a 3.0 prestige class, master siege engineer. As it predates Heroes of Battle, it doesn’t interact with those rules directly, and its abilities are most potent when dealing with multiple siege weapons used by multiple crews. Nonetheless, it does exist.
Back to Heroes of Battle, the legendary commander prestige class may be worth considering. It requires Leadership and expands on one’s ability to command troops. Leadership may even be appropriate for once since siege weapons require crews (ideally two for light ballistae, four for heavy ballistae, in addition to the crew leader).
Dragon vol. 310 provides a number variant fighters, including targeteer which gains proficiency in two ranged exotic weapons—Heroes of Battle does not define ballistas as exotic weapons, and Ballista Proficiency is distinct from Exotic Weapon Proficiency, but it’s a minor stretch to consider it. Alternatively, the commander variant in the same article may be more appropriate.
The commander and targeteer have different bonus feat lists from the base fighter, but it only covers core feats—it seems to me that non-core feats should be added to the list as appropriate, and these siege weaponry feats are appropriate for these variants. If the ruling is that they cannot be added, though, then of course you don’t want anything to touch that feat list, and base fighter is ideal.