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I'm having fun with two arena shooters on the dreamcast via flycast emulation: Outtrigger and Quake III Arena.
(hexbear.net)
These are awesome and you can play them super easy with the kb+mouse in flycast with a little tweaking. In both games assign your kb and mouse to ports b, c, and use "raw input" then play in full screen. Outtrigger is a bit wonky because you need to go in-game and tweak the settings to play with esdf movement, but it's simple just select the control type in game.
ANYWAY, you can also play them online via DCNET the revived seganet online service for dreamcast. Just download the nightly flycast build and it will automatically connect to the hosted servers! 
I know Quake has bots online, Outtrigger I've yet to find anyone to play with. But these games are sick as hell.
It's a third or first person arena shooter in the vein of quake, and yup you can emulate it and set up local matches against bots! Does your handheld have twin sticks? That's the best way to play on controller.
Yep, 2 sticks and a dpad.
You should be good to go then, just play around with the emu settings for mapping and such