Electronic – What wire to buy to extend the legs of SMD components

What you want is a Hot air rework station:

This uses a gentle stream of hot air (soldering iron temperature) to melt the solder and release the components. Also, a "hot plate" can be beneficial when working with such components as BGA chips:

Failing that, put it in the oven face down and let the components fall off. (may not work depending on component size - the surface tension of the solder may well hold them in place).

The other ones are answering about selecting wire, allow me to explain how to straighten a wire. It is very simple once you know how it is done.

• Start of with a long piece of stiff wire, it is probably supplied from a roll;
• Attach the wire to something solid near the ground, for example a central heating pipe. Make sure you can pull and turn it without the wire actually moving at that end. As near to the ground because you don't want to bend the wire once you're done by having to lay it down on the floor.
• Take as much wire of the roll as you can possible straighten in the room, leave couple meters room to move yourself around;
• Put the loose end of the wire in an electric drill, make sure it is tight enough so you can pull the drill backwards;
• Run the electric drill low'ish rpm, while slightly pulling the wire, twisting the wire along its length;
• You'll notice the wire will get somewhat longer and nice and straight;
• Stop the electric drill once you are happy with the straightened wire;
• Cut pieces at the required length from the straightened wire ...

I have no experience with steel wire, but it works wonders with 2.5mm² coppper (as in a home electric installation) and at work we used to do it up to 1 cm² for lightning rod installations, but we used a somewhat more powerful drill for that.