Steam Deck natively recognizes the PS3 controller. Simply plug it in via USB, wait for Steam OS to recognize it, then unplug USB cable and it will work over Bluetooth without needing
User manual Speed-Link Strike FX Wireless Gamepad (English - 2 pages)
Getting an original PS1 Controller to work on the PS3 : r/PS3
Mini Chat Board for the PlayStation®3, Jöllenbeck GmbH, Story - PresseBox
The best controller for steam deck is one you already have. My PS One Analog is still working, tho through cable with more than a decade old PS2 to PS3 USB converter.
How to Sync your PS3 Controller for First Use on your PS3 - YouTube