I would say, keep your ties as an accent and your general wardrobe full of neutral basics (whites/cream/ivory, light greys, dark greys, etc.). If you are keen to match your tie with your shirt, I would say go complimentary instead of direct tone-on-tone, which is the issue of your ties getting lost if they are too similar to your shirt color. Complimentary schemes might be a blue tie (cool) with a cream shirt (warm) or an orange tie (warm) with a light blue (cool) shirt. If your tie is patterned/illustrated, I would keep the shirt as one-color/blank as possible. And vice-versa, if your tie is a single color, you can play up your shirt with a subtle plaid or polka dots.
As far my company goes, when I started, we were "business casual" (J.Crew and Kate Spade) with "casual" (tshirt jeans) on Fridays. Then somewhere in the middle, we got a bit more restricted and went to more "business professional" (pencil skirts and blouses). Now we are "creative casual" and you can do whatever, so most of the times I wear jeans and graphic tshirt. Recently, I have been trying to live more minimally (I know there's another thread with this discussion somewhere) and that includes purging my wardrobe. So my current tactic is to get a lot of neutrals as my base and spice it up with a fun accent necklace or cute pattern on shoes (Old Navy is my go-to). I personally prefer working in the most comfortable clothes possible, but now that I am rising up the corporate ladder, I am in more meetings with important clients, so I try not to look so "hobo-esque" at work.