While you may be on a limited budget, skimpping out on a soldering iron is not a good idea. Low quality soldering irons will end up costing you more in money and time in the end. They are very likely to have tons of issues. It is a much better idea to go with a pretty good soldering iron and have a tool that will last you for years to come.
This is the soldering iron that many other users have and it's been thoroughly vetted. I personally use it and it has worked great since I got it.
It's also a good idea to get a conical or
pencil tip for it because it doesn't come with one.