I use Weller soldering pencils. Over the years, the tip and screw collar fuse to the end of the soldering iron. Unless you are doing something that brings solder and flux to the screw on collar, I doubt you are doing anything wrong. If you want to keep that from happening, periodically disassemble and lightly sand with fine sandpaper or steel wool.
Without going to Home Depot, I can't tell what flux they are selling. NEVER use solder intended for plumbing that uses acid flux. This will corrode your electronics. There are various fluxes that are suitable for electronics; the most popular being rosin. I don't know if they sell rosin-core solder at Home Depot and Lowes. If they do, you can use it. Other places you can buy rosin-core solder is Fry's Electronics and various mail order electronic supply stores like Digikey and Mouser.
You can use older tin-lead solder or the newer lead-free solders. Newer, lead-free solders avoid this health hazard, but could grow "tin-whiskers" that could short things out. The whiskers are usually tiny and for things like soldering wires together or soldering in decoders to your locomotives, the whiskers are not likely to ever cause you trouble. Lead-free solders generally take a little more heat to melt the solder than older tin-lead solders. So if you want the lower melting temperature and use tin-lead solder, just keep it away from children and don't eat things while soldering and wash your hands before you do eat something.
For more on soldering, see my website at: http://www.WiringForDCC.com/solder.htm
Wiring For DCC