For a soldering iron, I use a Hakko 936 I ordered from Japan a few years back. I recently had to replace the front electronics, but I think that was the exception more than the rule - I know people that have been using that iron daily for 20 years without a hitch. Besides, at $12 for a factory new replacement part, I wasn't exactly put off by the experience. For SMD work, I picked up a cheap Gordak 962 for $63 shipped. I wasn't expecting to win the bid. It's serviceable for my needs - I do mainly through hole stuff. This also serves as my back-up iron, as it's basically a Hakko 936 clone with a hot air station tacked on - it also uses Hakko parts and tips, so replacements are easy.
For desoldering, I normally use a Soldapullt sucker. I've done 128-pin CPUs with no real problems. With that said, I also have the Velleman tool that was linked by the OP - it's a good tool, and I pull it out when I need. I haven't had issues with it clogging, but I have had several issues with it not being thermally conductive enough to melt the solder properly. That said, though my experience is limited, it's by far the best one-handed tool that I've used, and I know guys that do vintage PC motherboard repairs for a living that absolutely swear by that particular unit, and they also have several different industrial/professional solder suckers.