Since you asked a more seasoned Retrogamer, I aswer, since I play videogames of all kinds for 40 years. The Logitech Gamepads look very cheap but I never had one in my hands - they might behave decent in your hands, but you get what you pay for and they actually look overpriced to me at €50 for the F710. An official gamepad of the consoles like Xbox, Playstation or Nintendo would work also fine and cost as much or slightly more, but will feel and perform much better.
I’d never go back to wired controllers if I don’t have to. It’s ergonomically much better and for your hand especially.
Force Feedback, if it will work ;), can be turned off with every application you can game or emulate. For example Steam or RetroArch have settings for that and I can’t remember or imagine a software for (retro) gaming without it.
I personally use many game controllers for different purposes, but for PC/Linux or RetroArch/Retropie/MAME I used mostly an xbox360 wireless pad, as it is recognised always and has a wide fanbase, meaning also the drivers for Linux are mostly in the kernel, so it’s plug and play. The Xbox One/Series will be similar I guess. I know form my recent research that the best controller based on lowest input lag would be a PS4-Pad, which needs bluetooth to connect and a cable to recharge. My Xbox360 wireless has a USB dongle and a 2,4Ghz Wireless signal, plus it features removable battery packs for fast recharge switches in the middle of the action. I prefer the later, since that is true wireless and it saves you a second pad to switch to.