Welcome: Personally I use black, charcoal or gray on everything I mosaic. Grout color is strictly a personal choice. Lots of artists use multi-colors in one piece very effectively. Don't believe I've seen the word tacky used on this forum re grout colors, but if so - who made that person grout police? It's the artist's choice, IMO.

It is as slow said personal. I am a fan of black charcoal or gray also-very rarely do I venture away from that.
Linda Smith (mosaicsmith) on her blog has a couple of good tutorials for multiple color grouts in a mosaic.
Painting grout-I have done it, you must use a wash, if you use straight undiluted paint it can look thick and unnatural, hence the tackiness you refer to. I would not recommend mixing up all the colors at once-it may set up before you get to use it! Heres some links. Linda, as an artist really has a fine instructional blog.
http://mosaicsmith.blogspot.com/2012/01/more-shading-grout-in-mosaic.html
http://mosaicsmith.blogspot.com/2010/04/thoughts-on-how-to-choose-grout-color.html
http://mosaicsmith.blogspot.com/2009/10/shading-grout.html

I too have painted grout many times but if you paint it straight on the grout with a brush, it looks ''unnatural'' somehow. What I do is I lightly sponge on paint with a sea sponge and then wipe off the tesserae with a terry cloth rag. Sometimes I do multiple layers of paint. Sponging it give me the soft blendy look I want.

Thank you for all of your help! I will post a picture of my mosaic when it is finished!