What makes a good soldering station
You don't need a $1000 iron unless you're going to be using it all day, every day, for a living, for the next 40 years.  Same as any other tool.  $100 will get you a good iron that will last you a long time (if you take care of it) and will do any hobby-level job.

Adjustable temperature is nice for versatility, but not necessary.  You can overcome a fixed-temperature iron's limitations with technique and practice.

Personally I spent the first few years going through inexpensive (sub-$40) irons before finally setting aside $100 for a Hakko station.  Things I noticed:


The control unit and soldering base were much sturdier/heavier, and didn't move around on me
The iron's handle didn't get hot after 30 minutes of use
Being able to adjust the temperature is nice when dealing with different heating needs
The iron heated up much faster
The iron sat with greater stability in its holder than previous ones
The included list of useable tips had like 80 varieties.  I haven't used any of them yet, but I know they're available if I need them


You can, of course, get by with inexpensive tools depending on your level of use and the types of projects you're doing.  Many projects are absolutely doable with a $20 35-watt iron.  To me, $100 seems just about right for a tool I use reasonably often at a hobby level.

Edit per recommendations from comments:


Temperature control (not to be confused with adjustable temp) makes it much easier to get consistent solder joints.  Temperature control means there is temperature feedback, so the iron tip will maintain its temperature when dumping heat into the joint (up to the power limit of the iron).  This is especially useful when soldering to something that sheds heat quickly (like a ground plate).
Having enough wattage is key to good joints.  If the iron doesn't have enough power to adequately heat the entire joint, you'll get "cold joints" which don't conduct well.  At best they're annoying and give unreliable behavior.  At worst they can be a fire hazard (they act like a resistor and can get very hot).


I submit that 35-40W is ample power for small projects that only involve small-gauge wire and component leads.  I've used a 35W iron for things like swapping guitar pickups and little circuits you assemble on perfboard with 20AWG wire.  More wattage is generally not a bad thing, as you'll generally end up with an adjustable-temp station above probably 60W or so (my Hakko is 70W).  For soldering to a big hunk of metal (like a large grounding plate or block), you may eventually need a 100-150W gun.

I certainly haven't taken a survey of every available option, nor used them all, so as always YMMV.