Guess I am late to the party. I use a dual solder station with a solder gun and a vacuum pump. The vacuum pump is great, removes all the old solder so can get the hole clean and ready for installing the new part. It makes those wicks and hand pumps seem like a joke. I can remove every cap and have all the holes clean and ready to reinstall a new caps in very short order.
Other tips I was taught and think it a good practice. The solder is not to provide the means to hold an item in place but only to make a better connection. All devices and wires should be attached in a manner that they are secure prior to applying solder. Heat the item to the point that it is hot enough to melt the solder, don't melt the solder to apply to the connection, but rather heat the connection to melt the solder. Use a heat sink to protect the device. After each solder point, clean the tip on the wet sponge and then re-tin your tip.
I use to use the Weller solder stations but I hated the cheesy metal tips they used, not sure what tip my station uses but it seems more like a ceramic tip as it always seems like new and clean. The station I like, and use is sold on Parts Express, and is made by Stahl, the tip they use is a PTC tip, and it always seems like new, unlike other tips that seem to get old and fouled over time,
And buy a helping hand, which is a heavy base with alligator clips to hold everything in place while you solder with one hand and feed the solder with the other. Leave the item that you solder in place for a good bit of time prior to moving it, as the solder needs to fully cool prior to moving it.