Your first concern is safety. You want to make sure the chair is sturdy and won't tip. Make sure there aren't any catches to pinch fingers. Make sure that tabletop locks good and can't be pushed off or unlocked by the baby. Make sure there isn't any belts or things that can be misused to get around the neck.
Stability (not easy to tip over), locking wheels, being able to adjust the height, reclining back for baby, vinyl cushions (easy-to-wash), a tray that slides off with one hand
You want to look for a cushioned seat, swivel wheels that have breaks on them and don't allow any sliding and a removable tray so that you can keep it clean. Anything that is removable and dishwasher, or laundry safe is a plus.
