Latest update here. Thanks to everyone who helped me out!

I have an Nvidia Shield hooked up to my TV, and it's great for Android games and emulation. I'm looking for similar hardware that will allow me to play my Steam library on the TV.¹ It doesn't have to be as small as the Shield TV, but I'm not interested in having a giant tower hooked up in my living room. Basically, I want what those old Steam Machines promised before fizzling out.

What I'm looking for:

• Pre-configured
• Able to support wireless controllers through Bluetooth
• Able to play smaller, less demanding games flawlessly
• Would be nice if it could play more demanding titles, but this is not a must
• Has decent cooling (I'm worried that boxes not designed for gaming will get way too hot)
• Price point: undetermined so far -- I'm willing to pay what I need to, but I want to see what's out there before committing to anything
• Would like to be able to set it up to basically be a seamless "console" if possible, where I can boot right into Steam (or easily get there with a controller) and not have to use a keyboard and mouse (I do have a Steam controller but I would rather use an 8BitDo SN30 Pro+ as my primary input method)

Searching around, here's what I've found so far:

• The System 76 Meerkat is a mini PC that looks great (and I'm partial to the company), but I don't know how it would perform with gaming. Also, I haven't decided if I want the (small) amounts of friction that come with gaming on Linux on my TV or not.

• Intel NUCs seems to be popular, and they have some gaming-focused models at higher price points.

• The MSI Trident 3 is explicitly gaming-focused and has a dedicated cooling system. Might be overkill for what I need though?

Here are my main questions:

1. What other hardware options are out there that I don't know about?
2. What hardware profile and price point should I be targeting for my needs? How little is too little, and how much is too much?
3. Are there any pitfalls to this kind of setup that I'm not aware of?

I'm open to any and all suggestions, as this kind of stuff is all a bit over my head so it's hard for me to even know what I'm looking for. I haven't even decided that this is definitely something I'm going to do yet, since there's such a wide range in price and performance. Instead what I'm trying to do is figure out what my needs are and then which models (if any) would fit them best.

1: I do have a Steam Link and have tried the app, but the quality for me has been spotty enough that I would rather have native hardware playing them than trying to stream it from my laptop.