Wire is fickle, so the best thing to do is to cut it in short lengths. Hold the very end as if you were sewing, and avoid at all cost rubbing your fingers along the length of the wire, because it will make it springier. Never use a length of wire that is longer than the length of your arm (hand to opposite shoulder, which is about 2 feet something).
And tug at the end of the wire, if it wants to curl. Always watch for loops. Do NOT let the wire loop, because that could potentiall turn into a “kink” and break the wire.

I always stick a finger or the thumb from the hand holding the work through the part that's being pulled through on a coil. I keep it rounded that way on the last tug through and it helps keep it from kinking.

The wire wants to cross and as soon as you see that happening, you can "rotate" the wire on it's axis to uncross it before you pull it through any further. That will take off some of the tension that makes it inclined to kink.

If I am working in an open design I will cut long piece of wire(much longer than most artists might)... what I do to make the piece of wire more manageable is make a coil part way down the piece so it does not interfear with my hand placement as I wrap... that way there is less wire hanging to get kinked and such. I wrap it in a coil like and that the end and wrap it aroung itself a little... like the way a guitar string is coiled comming out of the package. Hope that make sense... I guess if you don't play guitar, you might not have a clue what I am talking about LOL