I collect and repair 1st party controllers for game consoles, been doing it for a few years, and I have a good bit of experience with the DS3. Here's what I've learned.
Brook Wingman is probably the best, XE2 (Black) and XE (Pink). They support the home menu button and both can be gotten cheaper used on Ebay, got a XE2 for 30$ and a XE for 10$. Also works great with the DS5, I used the DS4, DS5 and DS5 Edge with it and all fully function with Gyro and menu button. If you also get the Brook X One for xbox one or xbox series X it adds Gyro to the Xbox controller so that you can use a Xbox controller with working Gyro for games that need it, both the X one and XE adapter are needed for this. You can not turn the console on with the adapters though, only the offical DS3 and maybe some clones can. I've setup my modded PS3 with Wake-up on lan, I use a SofaBaton remote to send a Wake on Lan message to the PS3 to turn it on if it's off (Had to make a HTTP to WOL program to do this), a modded PS3 also allows you to send controller commands over HTTP so I can control the whole PS3 with the remote including menu functionality.
Pressure sensitive buttons are rarely needed, few like Metal Gear 2 and 3 and Silent hill 2 and 3 really are games that benefit from it, Metal gear really might require it.
I have a lot of issues with the Dualshock 3 controllers. They are a bit of a pain to work on, putting them back together can require a lot of fiddling to get the triggers to work/feel right as well as aligning the button PCB membrane. Broken joysticks on controllers are nearly unrepairable since they use 4 pin analog sensors that no other controllers use nor is there a hall effect replacement that would allow you to calibrate at a hardware level (Unless you get the older model that uses 3 pins). There are a lot of fakes that look and feel like they are real but are barely functional when you use them. There are so many different hardware revisions of the controller that you can not get replacement shells for them unless you just get lucky, so no "easy" way to fix one with a broken shell or customize it to look cool. Mini USB.
But even with those issues, if you get one cleaned up with good joysticks they do feel right if you are playing PS3, PS2 or PS1 games. And they have a few cool special release ones (Can get expensive), I've collected all 4 transparent controllers and have the MBL and limited game release controllers such as the Xillia and God of war but also they have a lot of colors, I like a different color/style controller for each player to disguise them. I've figured out how to swap the Mini-USB to USB c, but also the official Sony charge dock is one of the best for any controllers I've used so I mostly leave the mini USB (Never swapped on limited edition controllers, just swap batteries). And there are some really good large Capacity batteries you can get for them (if you find not fake ones) that can bring the battery life upwards of 60hrs in my experience.
