Here's a video I used years ago to improve my technique for dying hair...
https://www.youtube.com/watch?v=fv2Io96heJU
She also has a trick about removing any stains from skin - it might be too late now but good to know if you do it again.
I've used boxes before where you mix things in a bottle and shake it up and then pour it on with the bottle. Nothing wrong with them, I used one for a long time and the only reason I stopped was because the company discontinued the color. But for the last several years I just go to Sally's and I buy a bottle of color, a bottle of developer, and then mix it in a bowl and put it on with a brush. Right now I'm doing bleached blonde that way. I own a mixing bowl, two different brushes (one is very small and fine for roots, the other is much bigger), gloves, a smock, alligator clips, and a cap. A few other things like combs and junk. It was pretty inexpensive to get it all set up.
It takes a little bit to learn how to do it IMO, I am terrible at looking in the mirror and knowing which direction I am supposed to move my hands and arms - but it's overall not really difficult to do, and I much prefer it to the squeeze-bottle method. The best part is that when it's time to do my roots, I can just mix up a little bit in the bowl and do it that way. They do make root touch-up kits but I prefer to have more control over the amount of product I mix up. I don't like wasting product so I love that I can mix up whatever amounts I want in the bowl and the color and developer stay good in their own little bottles until I need to mix up more.
If you hate it:
http://www.ulta.com/ulta/browse/productDetail.jsp?productId=xlsImpprod620020
This stuff works!
Coconut oil or baby oil should help you remove any stains on your skin, you may need to add a facial cleanser or soap to help. If the stains are persistent and your skin isn't sensitive you can use nail polish remover, but I would try to avoid that if you can!
As for grays themselves, I suppose I'm lucky, my natural hair color is a mixture of all different tones. Red, brown, blonde, black, gray - it's been that way since I was very small. I still remember being in grade school and flipping my head upside down to reveal all the gray hairs underneath (the top lightens up in the sun so it's not as noticeable.) So for me, I have never been concerned about it. I think there is a certain amount of accepting gray hairs as a part of your life, LOL, but at the same time I have always been pretty loosey-goosey with dying my hair and changing it. A few times I have been disappointed with a hair cut or dye job (always when somebody else dyes my hair...) but it is just hair and it will grow back. The grays will come back too, haha. So I think it's totally fine to dye your hair to hide them if you want, so long as you aren't obsessive about it or anything like that. I know some people who really stare at the mirror and freak out if they THINK they see one and immediately run back to the salon to have their hair dyed again... as always, there's a balance to life!