Based on size, you probably want a vacuum. Dust collectors are generally too large to pushed under a workbench. My dad has a few of the Fein vacuums in his shop (older models) and they are indeed very quiet. Festool has a fancy one that is also supposedly quiet.
If you’re a creative person, you can probably rig something up with a collector that is relatively compact. I use a harbor freight collector on a DIY wall mount with a cyclone and cart filter that is pretty compact, but it was a project to design and build. I also think a few companies offer a small wall mount collector (Woodcraft and Grizzly come to mind) that might work. Just note that the bag filters a lot of dust collectors come with suck for fine dust filtering.
What are you using for a dust boot? One thing with collectors is they are designed to move a large amount of air but don’t actually pull a large amount of vacuum, so they tend to be ineffective if the hose is necked down too far. If you’re running smaller than a 2.5" port you probably want to stick with a vacuum.