I'm using a Model 4 with 4GB of RAM, but 2GB would probably also be ok. (I haven't measured peak memory usage, but I imagine that having some spare memory for file caching reduces read contention for the SD.)

Home Assistant can take a minute or two to start up, keeping all four cores quite busy, so I wouldn't recommend trying this on an older model myself.

If you want to use the Pi's internal Bluetooth module, obviously you'll also need one that has one and supports Bluetooth LE. Again, I can only speak for the Model 4 here, which works great for that.

In terms of minimum requirements, you could even run that on a 0 or older.

In practice, you probably want at least 3b+ for reasonable performance. If you're buying new anyway and can get them for MSRP I don't see why you wouldn't get a 4.

If you want a Pi (or alike) for specific reasons, go for it!

But, if you are looking for cheap and relatively low-power compute, I strongly recommend looking at used ultra small form factor PCs. You can get much more computational power and expansion, often for cheaper than a Pi. And eBay is riddled with these things, unlike recent Pi availability.

https://www.ebay.com/sch/171957/i.html?_from=R40&_nkw=%28len...

The pricing gets even better if you want to buy them in a lot.