Hi
melissa
First off I would suggest trying a semi-permanent. Unless you're covering greys there is no reason to use a permanent dye. Secondly do not select an ash shade. It may not turn your hair green but you may not get the dark brown colour you're looking for. Thirdly, I would suggest trying a medium brown shade. It will come out a lot darker than you expect. Dark brown shades tends to go black (this is from personal experience). Do not use a warm or 'golden' shade if you want to tone down the brassiness in your hair.
I have naturally dark brown hair and have been colouring it various shades of medium brown over the last few years. I'm now colouring my hair at home and have been for the past year and I've used all 3 tones and neutral always comes out looking the most natural. I now kick myself when I buy ash toned hair dye to tone down any residual brassiness because it always ends up looking worse than before.
My suggestion to you would be to check out the semi permanent dyes from either the clairol or l'oreal ranges and choose the neutral medium brown. I've had the best experiences with both of those brands although I use john freida now but its a permanent dye. Garnier is also suppose to have good semi dyes. And just a tip never trust the hair swatches on the box nor the ones they sometimes have on the shelves.
Hope this helps x