Kisz4tj,
Tracey is definitely well-versed on this subject. Hopefully, I can also help a little. I am not sure exactly how dark your hair is. but if that rinse did not show up on your hair, then it is fairly dark. If you have dark hair and want to lighten it, you have to lift the color at least a couple of levels and deposit the lighter color. I am almost back to my naturally dark brown hair color, but I experimented a lot with color, going all the way to a light blonde.
A few of the ladies went into some of these products but as far as color goes you have 3 options: a rinse, a semi or demi permanent, and permanent. A rinse is basically colored water that rinses right out with rarely any permanent effects or damage. Technically though, there is not really such a thing as a semi permanent color or permanent color. Semi-permanents penetrate the outer layers and gradually rinse out. Permanents penetrate through most or all layers, depending on the porosity of the hair, and the type of chemicals used to lift. Often, semi-permanents penetrate the cortex of the hair shaft deeply enough to leave a permanent stain. And usually permanent colors fade, and very often fade a lot.
Your best bet probably, would be to go to a professional, especially if you don't know a lot about coloring and want to be on the safe side. I chose to do it myself with box colors. Now a word about box colors. You usually won't get what you see unless you are within a couple shades of what you are trying to get to. You will get a combination of your color, and the one pictured there in most cases. For light shades, you would have to use a bleaching agent and lift the color very light and then deposit the color you want.
In your case, since you want a reddish brown shade, you shouldn't have to work too hard to get it there. A semi-permanent shade should give you some subtle reddish brown shades. If your hair is in good condition, and you want a more dramatic change, you could look into a permanent color. I have found the best box color system by far is Clairol Textures and Tones. You will also probably get box-color or close to it with this one. If I remember correctly, it is ammonia and peroxide free , though you should check to make sure. If I would have found this brand earlier in my color experimenting process, I would have gotten the color I wanted right away, and without nearly as much damage. This was my experience, so I am not sure how your hair would respond to it.
You can also go over a permanent(and I think semi's) with a cellophane like Sebastians to get just the right shade you want, and to protect your hair and keep your color fresh.
Again, do some more research into coloring, and try to consult with a professional if you like. What works for some may not work for you, and you don't want to end up with damaged hair, so be careful. HTH