Originally Posted by Taowolf51
I do have a rosin-core solder. My guess is that my iron sucks, at times I have to wait a good 30 seconds to get the solder to melt.
Just for clarification, is this 30 seconds from turning on the iron, or is it with the iron already hot? Are you using leaded, or lead-free solder? (you should be using leaded, it's easier to work with)
As suggested above, tinning the connectors on the plug is important to promote better heat transfer, and you need to heat up the connector for a few seconds before you bring the wire in. This is because the connector has a large thermal mass, and if it's not hot enough, the cable wont actually 'stick' to it even though you may have seen the solder on the wire melt. Try and get the iron's tip touching both the connector and the wire as you're making the connection. You might be fighting an uphill battle though, it sounds like your iron's tip is heavily oxidised if it's having trouble melting solder while it's hot, you can try tinning the tip and cleaning it a bunch of times, it might help.
For your first decent iron, I usually recommend the Hakko 936 clone, you can find one here. It's a great iron for the money, just hop on ebay and pick some some extra tips, I'd say a ~2mm chisel tip for most work, and a big 4-6mm chisel tip for big jobs (thick wire, pcb mounted heatsinks and the like).
If you're looking to spend more, the Hakko FX-888 (or the 888D) is a small upgrade from the clone I linked, it's the de facto standard DIY hobbyist soldering iron. It'll just be more comfortable to use than the clone, and it'll have slightly better thermal performance.
Honestly, I don't think there's anything the FX-888 can do that the cheap clone can't, but if you like nice things, then it's okay to splash out for it.