Electrical tape glue wears out over time and will begin to unravel. Not the best method and butt ugly as well.
Soldering is easy. Buy a cheap solder iron and some solder, get solder with flux in it...makes it easier, at Radio Shack. Buy some heat shrink sleeves as well. They come in different sizes per wire gauge so buy the right gauge.
Cut a bit of wire to use as practice...practice makes perfect. Cut the wire ends, to be joined, to length, about 1/2" each is fine, slide the heat wrap over one end and up a bit of the wire length so it is out of the way. Twist the wires together, hold the heated solder iron against the twisted wires. Hold the end of a length of solder to the twisted wires, not the solder iron or you may get a "cold" solder joint which won't hold well. When the wire is hot enough the solder will melt and "flow" into the twisted wire. Let enough flow to penetrate the wires and turn the area "silver" but not so much to create a blob of solder. Now let the wire cool and wipe off the soldered wire with a damp rag to remove any flux, it is corrosive but not a danger problem. Slide the heat wrap over the new joint and use a heat gun to melt the wrap. If you don't have a heat gun a small propane torch, what plumbers use to heat pipe joints, just use the heat not the flame hehehe.
I like banana connectors and use a type that has a screw top so it is reusable. They are by Monster and are $20 for 2 pair and are a bit pricey but I like them. There are other similar types and brands and they generally all work and are worth the cost in my opinion.
Good luck