If I were to start over again, I'd probably get a few of
these and the cheapest set of resistors I could find, and would start soldering away. That's probably the cheapest and easiest way to practice.
But building those small kits I talked about in the other thread, albeit a bit more expensive, was incomparably more fun. And it also taught me a lot more than just the soldering technique.
For desoldering I use an Engineer SS-03. It's extremely well built, very easy to clean (which you rarely need to do, because it's mostly self-cleaning), and works really great. The silicone tip is awesome. Sure, a dedicated desoldering station would be faster and more convenient, but I'm getting along so well with this little pump that I never had any reason to consider upgrading. I can desolder anything with it, and quite easily at that.
As usual, it's all about technique. As tempting as it may be to cover the whole joint with the tip, because the flexibile silicone tip allows it, you shouldn't do that, because then the pump won't be able to suck the solder. The soft tip makes such a good seal, that the vacuum causes the tip to stick to the board like a suction cup, and when you pry it away it won't extract anything. You need to leave a small gap, to allow for some airflow when you release the plunger. This may be common knowledge, but for me it wasn't and I learned it the hard way.

Also, what helps a lot, especially when desoldering commercial stuff made with unleaded solder, is to add extra solder to the joint beforehand. It may be counterintuitive, but the fresh solder helps enormously with the heat transfer and melts the old solder in no time, even at leaded solder temperatures. Don't worry about the pump having to suck more solder at once. It won't mind. It can, and it will. That soft silicone tip, when placed correctly, allows it to suck an impressive amount of solder in one go.
Spring-loaded desoldering pumps have a bad reputation, which is mostly well deserved, because most of the cheap ones that you will find for a few bucks in hardware stores are crap. But this Engineer has nothing in common with those apart from the working principle. It works like a charm.