I thought big boxes were the way to go, and have currently have me a Hana50, a Sig 100W+ and got an iStick 50W on the way. They're great for heavier duty coils, but I've found my daily driver in an 18650 copper mech and a well set up Derringer. Never thought I'd see the day I was shunning tanks and passthrough charging in favour of the footery drippers and battery changes. The boxes tend to stay in the house, and I'm gonna keep the iStick and a good size tank for those days when I need a good long distance setup. 4400mah should be ample for a good day's run time...
Back to your coiling question, I find it much easier to work with the thinner wire when you've torched it before working with it. Even a cheapo jet lighter should be up to the job of heating it enough to take the springyness out of it. Straightening it in a drill works, but it's still quite resilient and likes to expand when you finish wrapping your coil. The drill thing is brilliant on the heavier gauges of wire, especially when you start doing daft builds.
As everyone else had said, check your resistance and for shorts, chuck it on a mod and give it a pulse to heat and position it. Don't be too scared to manhandle it a wee bit, you'll find it's quite forgiving (within reason) and can take a good bit of wiggling/squeezing/poking around once it's been heated.
Best thing to do is keep at it. My toolbox sits next to the couch and it's become quite a hobby while sitting watching the telly at night to try out some new builds. I've got a wee dooket in the top where all my older coils go once I've got fed up of them so they can be fitted back in at some point. Experimentation is the name of the game!