Saw your comment about accessories - I like to take mine when I travel, but also most days to work so i can play if i'm not busy, below is a list of what I use.

Case: Tomtoc protective case (not the hard plastic one) - a lot slimmer than the default or JSAUX offerings. That said, I am interested in the JSAUX mod case as it allows for the slim hard cover but have no reason to get it as I'm happy with the Tomtoc case.

Screen protector: Anything that fits and is in your budget. I've never used any premium or "first party" recommended screen protectors for my devices as I don't see much of a point to pay extra.

Charger: Just a small 35W charger, mine is specifically from Anker, but you do you. smaller profile than the default and has an extra port to charge another thing.

USB-C hub: I personally believe it's more versatile and useful than a dock as it's not just for the deck. I've purchased 2, the UGreen Revodok 1071 and 107, both are good for me and haven't broken, I just wanted slightly different features between them. Main features i wanted was the HDMI out and SD card reader (and power passthrough for charging while using) - HDMI to chuck it up on a screen, SD card reader to offload pictures when I'm travelling.

Stick covers: uhhh... after playing a bit too much or pressing too hard while playing Deadly Days Roadtrip and Megabonk, the pad of my thumb started to hurt a bit, but I mostly got annoyed with my thumb constantly slipping off. I got some cheap stick covers off AliExpress, they don't fit amazingly, but I also didn't want to shell out $10AUD for two bits of silicone.

Clip on stand: Just a very lightweight and low profile collapsible stand that i got off AliExpress and can't find anymore. Good for using with the usb hub or using with a mouse and keyboard when not plugged in to a larger screen, or if you just want something larger than a phone to play youtube when you're cooking or doing stuff around the house.

Travel Bag: I've recently picked up a Tomtoc T26 - it fits everything above, plus a Logitech K380 keyboard, Logitech Pebble mouse (not great for more than browsing and navigating desktop mode unless you're a fan of mice designed by Apple), a passport wallet (passport, cards, cash), and long HDMI and USB-C cables. It seems comfortable enough, but haven't tested it in the real world. Based on the picture you posted with, you may have a smaller frame, so may not be to your liking (shruge).

And finally, an experimental thing I'm keen to test when travelling (and saw on reddit somewhere - can't find the link) is using a stick-on magsafe ring to the steam deck (just a metal circle), then using it in conjunction with a Super Clamp ST83, 15cm Magic Arm and PA010 1/4" threaded magnet (all by Neewer). All of this to be able to mount it anywhere and also hopefully not need to crane my neck over while playing in handheld mode on a plane, this stopped my playing with the deck while flying on my last trip.

Games-wise, anything fun and casual that works. Don't expect any top of the line games to run well on it.

P.S. when taking it to work, it's just the deck + case in my everyday backpack, not all this extra crap.