Not to bury the lead: no, you can't build a steam deck for under 200 bucks.
But now with that out of the way, what if you could? Now a Steam Deck very specifically plays steam games, and can do so natively, which is why it's very big and very beefy and also very expensive. Rather than seek a device that can do this, I'm instead looking for a steam deck like "experience" where you can play games on a handheld. Early disclaimer, when I say build really this is just using off the shelf devices and prepackaged softwares and putting them together in novel ways. I'm not an engineer, I didn't build any of the hardware or develop any of the software. But I am at the very least flashing a firmware, and I'm pretty sure that makes me a master hacker.
The device we're going to be using is the Anbernic RG556: It sells for under $200 and I managed to get mine on sale on aliexpress for $178.
Note: not my hands nor my image.
This is what it looks like out of the box. It's basically last generation smart phone without the extraneous pieces like cameras or cellular radios, encased in a shell with a built in controller. It's running a version of android and... that's basically it. What you see is exactly what you get, it's a phone that's stuck in landscape with a controller built around it.
Anbernic is a chinese based company that makes a lot of handheld devices intended for use with retro game roms. I've owned quite a few devices made by Anbernic and loved them all, but they were all linux based devices and this is the first one I'm trying that's running Android. The biggest benefits of this device are going to be it's honestly amazing quality 1920x1080 5.48 inch AMOLED display screen. Now, when you're dealing with devices meant to play strictly older retro titles, a large resolution and wide screen aren't necessarily always what you want. In fact this same device comes in another configuration called the RG Cube that has a 1:1 screen ratio that I would recommend if you are strictly playing 4:3 content. The benefit of having a 1:1 screen ratio is perfect pixel upscaling.
But that thing doesn't have an AMOLED screen, and this thing is beautiful:
Taking pictures of oled screens never looks as good as they look in person, but trust me when I say this thing is pretty. Also technically I'm cheating here but more on that later.
The biggest drawbacks of the device is that out of the box, even though it has pretty decent hall effect joysticks, a software error in Anbernic's firmware treats them as dpads and thus they will only give cardinal direction inputs. Luckily this is easily fixed, so long as you are comfortable with unlocking the bootloader. Luckily these chinese mobile devices are pretty easy to unlock, and we'll be flashing a modified version of anbernic's android onto it that has the joysticks fixed.
You can find everything you need to unlock the bootloader and apply the fix right here:
https://github.com/TheGammaSqueeze/Bootloader_Unlock_Anbernic_T820/releases/tag/release
If you're not comfortable doing this kinda stuff this probably isn't the device for you, because we're gonna need a lot more tinkering.
Once this is done, your next step is going to be to uninstall every single piece of software that comes preinstalled on this thing. It also comes with a shady unbranded SD card full of roms of dubious quality, throw this thing away. Trust me, all of these roms are going to be misnamed, corrupt, wrong region, wrong language... I love anbernic but they are a shady chinese bootleg company and this is just the price of entry. Throw that sd card away (it has incredibly poor write times anyway and will likely die in a few months) and provide your own SD card and your own roms. I'm using a 256GB micro sd card because that just happens to be what I had sitting around, and that should be more than enough. Even after adding my entire rom collection to it I still had 30gb of room to spare.
Once you've uninstalled everything, it's time to install the proper emulators and software. Load the device's web browser and download the retroarch apk directly from the website, but pretty much all other emulators can be downloaded from the google play store.
I recommend retroarch for everything up to ps1. M64 plus for Nintendo 64 (you'll want to spend $5 for the pro version here), melonDS for nintendo DS, ppsspp for psp, dolphin for gamecube and wii (only some wii games will work well on this) and netherSX2 for PS2. Once you have all of this you'll also need to open each emulator and set up your key mapping, doing it now will save you a ton of time in the future. Citra also works really well here for 3DS emulation, but with Daddy Nintendo having shut them and yuzu down I can't really link to where to find that. You're smart, you can google shit, you'll have to manually add that apk yourself.
Once all that's done, you've got yourself a powerful little emulation device with just one flaw, it still runs like a fucking phone. The android front end isn't all that great for a console experience, so we're going to replace it with something called daijisho. Download this from app store, go into settings, go to default apps, and replace your default home app with Daijisho. Now every time you load up this device you'll go into the daijisho front end rather than the android front end, which looks like this:
Just tell Daijisho what platforms you are emulating, go through each one and point it to the appropriate folder on your SD card to find the roms for it, and you can even set custom emulators for each game through this, if you find that some games work better on one emulator than another. Congrats, you've got yourself a powerful little handheld that honestly rocks my socks every time I pick it up.
But how was I playing Spider-Man? Well, I did say I was cheating, and that was through game streaming. There are android apps for steam link and playstation remote play (and xbox remote if you swing that way, I guess) and they work really well on this device with that beautiful bright display.
And the final big benefit of using an android device that I never thought of before... really fast sleep mode and suspension. Since all of these are native android apps, they are all built to automatically go into sleep mode when you hit the power button. This has lead to great pick up and play potential when using this thing, and is something even the steam deck sometimes isn't all that great at (it will sleep but it drains battery like a mofo while sleeping).
So there we have it. A steam deck (kinda) for under $200 dollars.