Also, if the solder used is not lead, e.g. ROHS compliance, it is going to require soldering iron with more power.
I am using 40W iron from Weller, and it works fine. But with more power, it is easier to ruin your PCB by overheating the joint.
For desoldering, I am using Radioshack 45W desoldering iron. It is a soldering iron with attached bulb for suction. I prefer this tool over solder wick, because the solder wick never worked for me. I tried the wick with and without liquid flux, it didn't really work for me. Maybe I should have used flux paste, but since I have a working tool I like, so I didn't investigate it further.
I think it would be wise to get a proper tool, because I have failed trying to fix things cheap. I tried cheap ebay soldering iron which died on me after couple of minutes. I tried other cheap iron and the tip oxidized and didn't hold any solder.
So, if you are not going to spend significant amount of money on tools, I think it would be wise not to start. Because if you start with cheap tools, it is likely that you would end up spending more money to correct what you have started.