The main thing you need is knowledge of the tip's temperature, not "what power am I pumping into it", as that is a parameter with no function, as will possibly also become clearer a bit further.
Decent brands will very likely keep existing and usually have replacement tips nearly infinitely. My personal preference is Weller (by Cooper Tools). To name an example their WTCP series of devices and tips and replacement heating elements are more than 30 years old and still available. Decent brands do that, because they know quality and service are still appreciated in these job segments.
Again referencing the WTCP, also known as MagnaStat, we knew the tip cannot be given more than 48W in those, but they used the paramagnetic properties of a material to make a tip that would regulate the temperature itself. Tips came in a range of numbers from 1 through 0, where a higher number meant a higher temperature. All you had to do was change the tip to get a different temperature. Since 30+ years ago making actually adjustable soldering stations was an expensive hobby, this was the next best thing.
For my demo ware and workshops I still use and maintain 6 MagnaStat soldering stations, though they are a bit closer to $250 each, their longevity makes up for it easily to me. One of them actually is 22 years old.
As a side note: I use the MagnaStats, even though the WSD series is hardly more expensive and has a settable temperature, because there's nothing a young child can screw up. I used to bring my WSD81 along with the two MagnaStats back before I bought the new ones and on the WSD81 I could lock the wheel (no longer an option I believe) with a key, but it took less than 3 workshops for the teeth on that wheel to become smooth in the 200 to 400 region. I have also had to replace that knob when it got ripped off and was lost "because it didn't rotate properly". Then when you leave it unlocked, you get loads of overhead of kids first turning it to 150 and then complaining that it doesn't work, or turning it to 450 and having hot flux burst out onto their hands.
All that said, will the handle get warm? Yes. The handle is holding something that's several times the boiling temperature of water, it will be at the very least slightly warmer than ambient. Will it get annoyingly hot? That depends on the brand. When the brand allows "20W or 40W" as "temperature" settings, I give it higher chances that it will become annoyingly hot than those brands that actually realise what units normal people use for temperature. The heat that leaks away into the handle depends a lot on the construction and between brands and even between series within the same brand that will differ. However, again, a decent brand will make sure the handle never gets warmer than, say, a hot bath and will usually restrict themselves to a thermal rise of 5 Kelvin under normal circumstances.
Whether you need a certain wattage, again, depends on the build of the soldering iron and the tip. If a lot of energy gets lost on its way to the tip, for lead-free you'll quickly need 60W to work comfortably with lead-free solders. On the other hand, with my Weller Micro-soldering iron (I have about 10 Wellers in my lab, if you also count the 6 demo units), it's only 35W and works fine for lead-free (small traces and what not), without even getting the handle slightly warm, because it creates all the heat right at the tip.
So, what I suggest is you find a website in your region and language that allows you to list and sort soldering stations. Find a group within them that allow you to actively decide temperature, either with a control knob or by replaceable tips. Because then the maker of the device thought about temperatures and what they mean, not even because you want to adjust it. And sort for cost.
Pick out the ones that seem and sound good to you and find reviews from reputable bloggers or reviewers like Mike's Electric Stuff, or the EEVBLOG's Dave Jones. They don't know everything, but they have worked a lot with those kinds of devices and will at least easily sort out the absolute worst crap.
For lead-free contact soldering I personally prefer a tip-temperature in the 320°C to 340°C with a good soldering iron that gets the majority of heat into the tip. If they are large objects or the iron is a bit hinkier you may need to set it to 360 or 370°C to compensate for the high losses between heat-sensor and tip.