With lots of riders trying to get into indoor cycling, lots are going to want to get the cheapest set up they can. I went out to find the cheapest set up, and here is what I found. Note: these prices can definitely be beat by buying used, but this is given the buyer would like to purchase new items. Prices will also vary depending on the sales being offered. This is also granted that the rider already owns a compatible road bike. All currencies used in this article are in USD($)
The Trainer
In this section, I will be highlighting a few different options. An option that only requires a speed sensor, and an option that will offer power data, allowing for a more accurate ride. In terms of power measuring trainers, a direct drive trainer that isn’t smart costs about the same as a smart wheel-on trainer. So it will ultimately come down to whether you want to prioritize accurate power, or a more accurate ride.
Wheel-on trainers are super portable and convenient, but I was never able to get a good amount of resistance on my Tacx Vortex. Since then, trainers really have not changed much, and the technology all remains the same. For the direct drive option, Kinetic offers their RS Power Bike Trainer for $329 bundled with a HRM(bonus!) or $350 without any additional accessories, and $379 with a cassette.

Currently, the cheapest wheel-on smart trainer is the Wahoo Kickr Snap or Tacx Flow. Both can currently be found for $299(this is with current deals).
Note: direct drive trainers require a cassette in order to function. Wheel-on trainers do not. However, many direct drive trainers include an 11-speed cassette with the purchase.
Device
Apple TV is definitely the cheapest and simplest option for those who are looking for a completely separate Zwifting device. Based off of my research, a 4K TV can be found for ~$200. The Apple TV 4K 2nd Generation(one version prior to the current), can be found for ~$100 or less. Bringing the total cost of the device to $300. Expect this price to vary as sales come and go. Note: the Apple TV 4K does not require a 4K tv to function, an HD TV will work just fine, but won’t take advantage of the full visual benefits of the ATV 4K.
Zwift Subscription
A Zwift account is free to create and comes with a 14-day trial. However, a monthly subscription costs $14.99/month. For riders under the age of 16, Zwift is completely free. Parents can read all about kids accounts here: https://zracecentral.com/all-about-zwift-kids-accounts/

The Totals
After all of the costs, here is what riders should expect to pay.
Direct Drive(not smart) —> $329(trainer) + $300(device) + $14.99(Zwift subscription – one month) = $643.99
Direct Drive(not smart) —> $299(trainer) + $300(device) + $14.99(Zwift subscription – one month) = $613.99
Summary
In conclusion, Zwift is not cheap. However, many Zwifters do not actually have to pay the amounts listed above. This is because most Zwifters already have a device(iPhone, Android, iPad, ATV, PC, Mac, etc) that they can use for Zwift, splitting the cost in half. In addition to this, deals on used trainers can often be found on sources such as ebay, allowing riders to find better equipment for less.