mandatory:
1) connected via USB and recognized by windows/linux as standard gamepad, without additional drivers
2) 6 buttons under right thumb, like on sega genesis and sega saturn controllers (the only requirement that sony dualshock 4 v2 and xbox one controllers do not fulfill)
3) 2 analog sticks and 2 analog triggers positioned like on sony dualshock controllers (not like on xbox controllers) and with minimum possible dead zones (would like it to be as good as on sony dualshock and xbox controllers)
desirable:
1) a LOT of extra buttons (recognizable as extra gamepad buttons, not duplicates of other buttons) in all imaginable places except where they are prone to be pressed accidentally or otherwise get in the way (in place where sony dualshock 4 has touchpad, between analog sticks, between analog triggers, underneath like on xbox one elite controller etc)
2) detachable USB cable, preferable with micro USB connector on gamepad's side, USB type C and mini USB are also acceptable
3) ability to work as both wired and wireless, rechargeable li-ion battery that can be replaced without tools, ability to work as wired device when battery is removed (sony dualshock 4 v2 fails this requirement)
4) all-matte case without glossy parts
would be awesome but do not even hope to get:
1) 4 separate buttons in place of d-pad or at least d-pad that looks like 4 separate buttons on the surface like on sony dualshock gamepads
2) keyboard like "chatpad" for xbox controllers
3) small steering wheel between analog sticks
4) nokia BL-5C or other "standard" (widely available) battery instead of proprietary battery with unique shape that has no other uses
does not matter:
1) brand (as long as analog sticks and triggers do not have dead zones and other major issues)
2) price (well, almost)
3) weight (300g is still not too heavy for me)