I'd second the TS100. It's ~$40 (given you can find a power supply for free, laptop bricks work fine. I'm using mini photo printer power supply which I found on the street + $1 plug + $3 worth of heat resistant silicone cable).
Warms up in seconds, open source and customizable firmware, takes very little space (kind of important to me since I don't have a dedicated shed/garage for the hobby). What's not to love about it for a beginner?
Apart from reading the buttons that control the device and writing the display, a digital iron needs firmware to control the feedback loop that maintains the temperature. Digital irons generally have PID based temperature regulation, unlike the crappy analog ones that have open loop systems (some analog irons have temperature regulation, e.g. Weller's old magnetic tips, but the crappy $5 irons do not). This requires a controller to supervise, but also means the iron heats up much faster and maintains that temperature while soldering.
Other features like a temperature graph or adjusting calibration and control parameters are handy additions when you have a nice display like in the TS100. Realistically though, people aren't really writing their own TS100 firmware with the exception of a few tinkerers. What it comes with is good enough.
Can you say where you can find a TS100 for ~$40? The cheapest I'm seeing is $50-55.
Also, are there different versions you need to worry about or are they all the same? I assume you only want a "MINI TS100" vs. some of the other knock off brands.
Warms up in seconds, open source and customizable firmware, takes very little space (kind of important to me since I don't have a dedicated shed/garage for the hobby). What's not to love about it for a beginner?