My personal favorite are the Stowaway brand by easycare- lots of models, all designed not to bounce much and easycare has great customer service. One trick I have used on my endurance saddle with a dressage style rigging system is to take the long strap, run in behind the pack rather than lacing it over the front and only attach it to the buckle that lets you tighten it. This will basically make the strap into a long loop. I then clip the strap to the buckle / buckle keeper on my girth and tighten the strap as much as needed. Much easier to attach/detach the pack and it doesn’t bounce around.
out of the stowaway models, I’d avoid the deluxe model - unless you need 2 water bottles and a good amount of storage in front, they will proably be too bulky. I have found for that for a quick ride , easycares “boot bag” has plenty of room for keys, phone, camera, sandwich and a small water bottle and is easy to attach in multiple places( but it would probably work best behind the saddle, not in front )