Having mentioned the characteristics needed of the wires for inclusion, this is a description of the good and bad points of some common wires used as inclusions within glass.
Nichrome (nickel chromium) is a generally favoured wire, due to it easy workability, ability to hold up in the kiln and maintain its strength afterwards. It does turn dull after firing, but can be cleaned up with a brass wire brush.
Copper is a softer wire to use, and exposed parts tend to be weakened. It may tarnish or change colour. Some twisted/braided copper can work better than single strand copper, but test first.
Sterling silver will work, but tends to scale and needs to be cleaned after firing. It can react with the glass and change colour. It tends to be soft after firing.
Fine (pure) silver works better than sterling, but even more prone to react with the glass - turning yellow. Some glasses (French vanilla and certain reds) will also change colour when exposed to silver.
Stainless steel is very stiff and hard to work with, but can be fused if desired. It retains its strength and if of the appropriate grade requires only treatment with a brass wire brush.
Gold or platinum wires will work, but are very expensive.