+1 all the advice to use lead solder. For small work, you allude to, i use .031 44% resin core Pb solder. Soldering iron is important also as many point out. You need a temperature controlled solder iron. For Pb, 700F is about right. The temp may be why you have a ball of solder at the end of the tip. I use a temp controlled tip rather than the temperature controller box, it is not important just a personal preference.
@bdial link to soldering equipment and how-tos looked nice. the temp controlled iron they had looked good and is a lot less expensive than my weller. If tips are readily available then it might be a good choice.
@Luckless had great notes.
Use the wet sponge every time the iron is withdrawn from the work, and just before tinning the tip. keep sponge wet.
Except for being tinned, solder should not be globbed on tip when put to the work. The iron is not for applying solder, but just for heating the joint.
Also before tinning the tip but after cleaning with wet sponge, i dip tip of iron in a little resin paste.
Heat both metal parts (wire, pads) just enough that the solder will flow - first. Do not apply heat for too long. Only then, feed just enough solder to the joint (not trying to feed the iron) as the solder melts. Not very much will be required. It should flow well and mold to the work being soldered. remove solder feed and heat. Joint really should have a shiny surface when it cools down.
Heat sinks when they can be applied between leads and component case will save destruction of the component.