Iam only going with the more expensive brands like weller.(very expensive) From my point of view i cant recommending cheap brands. And i totally avoid irons that uses screws to tighten up the welding tip. Mostly when the iron heats up the screw would loose it self. Most important thing is if you choose a high expensive brands, you always find replacement tips and having a longer support range (assortiment) of your product. And also the range of different kind of replacement tips are much higher on expensive brands, then the cheaper ones... The cheaper ones, doesnt perform mostly that good, range of tips are limited and also mosly hard to find.

Good stuff costs you a lot of money.. Actually there isnt a middle way..

I dont know in which country you living on.. So brands will specific in which part of the planet you are on.

Good brands are; Pace, Weller, Hakko. But they would cost you a fortune.

I have also an Aoyue desolder station here.. I cant recommending it if you want to use it for fine solder pads.. It only works great (a sort of) when you want to desolder thinker / normal bigger solder pads.. But avoid it for finer rework, because there are no finer tips for it available.. Only the expensiver brands have...
As on the Aoyue, it doesnt work / great on cpu sockets, IDE headers, memory sockets ect.. Works good on removing an AT style of keyboard socket, or motherboard psu connector. On home electronics like radios, tv`s it would work great, but on computer hardware you need more the high quality stuff.. Every factory that producing motherboards or computer cards using HQ stuff.. The downside of the Aoyue is the stability of the temps..
When its new it would work fine, but after some use the stability would just worse.. Often it stays to cold to work with..

An weller solder iron would costs you about 200-300 euros. But the problem with desolderstations is the vaccuum.. The cheaper ones would require a seperate air compressor and installation on tubing to create your own vaccuum installation.. Only creating one, you need to have the knowledge.. For home users this isnt ideal also because the compressor makes a lot of noise..
Its more ideal if the desolding station have a vaccuum pump installed in the unit.. The downside of this is that it would raise up the price of the whole unit..

For me the ideal way is go for the expensiver way with the vaccuum pump installed, so i dont have to worry about how to make my own vaccuum installation, and wouldnt require an addition of a small noisy air compressor.

I agree with Robin4, Pace/Weller/Hakko are the best brands you can get. I use a Weller myself with a 50W iron, but I've been thinking of upgrading to 80W. Weller is horribly expensive though.

The most important features to look for are temperature control, power, and avaliable tip sizes. Temperature control is most crucial, and with a temp controlled station, more power is better since it'll be able to maintain a stable temp even while soldering large surfaces (like on ground/power planes, which I think is what you're having trouble with).

If you looking for a solder iron the weller WSD series would be just fine for all your soldering work..(i self have a WSD-80 digital here)
https://www.youtube.com/watch?v=mOsZDQU2qPw
The pros for the digital version over the analog would be that the digital version is much preciser to set it to the actually temperature. But the analog version would also work fine if you are limited on budget..All of these versions are ESD free. But for an de-solder station i would keep in mind where you want to buy the replacement parts from..
If you want to buy a pace one (yes they have some cheaper ones) But if you need to order your replacement in america, and there is no dealer in europe then you had made a wrong decission of buying that brand..
I also doubt if i wanted to buying a pace or going for weller.. The Pace have a good entrance price-value when entering this marked but could give some problems when needed replacement parts.. And maybe they are more expensiver by the dealer in europe where you maybe live, and much cheaper in america where is a big heap of replacements available.

What also a good investment is, to buy a good solder fume filter unit.. Dont trust those things listed on ebay that you have to place near your to solder object and having an fan inside.. Yes these thing remove the smog from your solder work, but actually blows inside of your room..
For a good filter you may need something like this:

An basic version would costs you about 600-700 euros.. Also the gas filter isnt very cheap with 150 euros or so (this filter you have only to replace every year with full use..)

Or if you are handy, you can make from an air blower or something to lead it outside of your house with some hose to connecting to it...

A fume extractor isn't really going to be necessary unless you're soldering for 8 hours a day, 5 days a week. Just have a window open, or a fan running, or something like that, to keep the fumes away from your face.

The "go-to" good soldering iron for hobby use seems to be the Hakko FX-888D, which can be had for under $100.