David,
I’ve tried the streaming/casting and even wired HDMI option from smartphones and iPod Touches and it’s typically a letdown. Not necessarily for raw graphics but there are “hiccups” that break immersion - lag, disconnects, out-of-sync audio.
I typically use Zwift on an iPad with the Tacx handlebar mount (modified with a phone holder for using the Companion App) and it’s just so compact and convenient.
I also have an AppleTV 4k and can vouch for it - if you have an existing TV, I’d say go that route.
If you have to buy a TV or monitor, the price might creep past that of an Apple Certified Refurbished iPad. Use a site like RefurbTracker to alert you when a unit you want is in stock: https://refurb-tracker.com/
You don’t need a current iPad though I’ll let others weigh in on how far back you can safely go and still get reasonable performance. (certainly two generations, maybe more)
If you don’t want the iPad on your handlebars (it does wiggle a bit when sprinting, but it’s still secure), there are floor stand options, and you can still have your phone on the handlebars to run the Companion.
Circling back to the ATV4k though: if you’re thrifty and find a used TV or monitor for next to nothing, it’s a viable alternative to an iPad. Oh, I forgot to mention: you can get refurb ATVs as well, saving a few bucks there.
EDIT - while there may be cheaper ways to build a PC, one of the appealing things about ATV or iPad is “they just work.” I don’t think I’ve seen a crash of any kind in 2 years. Click the app icon, Zwift opens and works. No drivers to update, no faffing about with a mouse. No, you won’t get ultra-level graphics but, IMO, that’s secondary to “jumping on the bike and riding.”