I'll start off by saying that I hate mechanical keyboards with a passion. That said, Logitech MX keys - silent(huge deal for me), short travel space also sturdy, sets you back around 80 bucks. Mouse - Logitech G205 if you wanna stick to the 100 bucks budget with a wired mouse or G305 if you are willing to throw in an extra 10: Light, comfortable, snappy, can sensitivity can be adjusted at the press of a button, incredible battery life.
I hate the long travel distance and I hate noisy keyboards and they are uncomfortable af. They feel and sound like an old soviet typewriter like the ones my grandfather used to have.