Disclaimer: I hate the classic white shirt. If you have to be uber conservative, go with a light blue and throw on a red tie. That's classic and powerful.
More general advice: Your suit sounds fine. Black accessories are always a safe bet with grey. You can do brown if it's the right brown with the right grey, but you may just want to err on the side of safety and stick with black.
Shirts: I prefer solid color shirts simply because they are easier to pair with more ties. If you have checked or striped shirts, that's fine. Just remember when wearing such a shirt you have to limit your other patterns. A general rule of thumb is no more than two patterns. What I mean by this is you can wear up to two of the following that have a pattern: suit, shirt or tie. If your shirt and suit are patterned, your tie should be solid. If your suit and tie are patterned, your shirt should be solid. Etc. In general, I'm a fan of bold shirt colors, but for a job interview you should scale it back. Soft colors are widely available now with pinks and purples being especially popular this season - just remember, you don't want pastel. You want a soft color that doesn't look like it should only be worn on Easter.
Socks: should match your suit, not your shoes. Additionally, if you're feeling adventuresome, you can wear socks that match your shirt (so if you wear a green shirt, then a similarly colored green would be appropriate) or on occasion your tie. If you go the socks-match-suit route, your socks should be one shade darker than your suit.
Ties: Keep it simple and you'll be safe. A solid color tie is always a safe bet and so long as you have a basic understanding of complimentary colors, you'll be fine. If you must go with a pattern choose something simple. Stripes are usually a safe bet, so long as the stripes aren't mixing in more than two other colors. A simple pattern (no themed ties a la flags or golf paraphernalia) or even a nice paisley tie (if you can find one that matches your shirts) can add some vibrancy if you've opted for non-pattern shirt/suit. White ties are a no go for work, and consequently interviews. A black tie, however, will be your best friend. It pairs well with a variety of colors and adds a distinguished look. Consider getting a regular black tie as well as a skinny black tie (note the skinny black tie should only be worn for those that aren't too much larger than average - if you're carrying too many extra pounds the skinny tie will look cartoonish and fail to give an adequate visual break to the shirt/suit like it's supposed to). Note that a red tie is classic, especially when paired with a light blue shirt. Finally, I'm not sure what you mean by "chunky" stripes, but in general I'd opt for a medium stripe - neither too narrow nor too broad. The important thing about striping is to remember that your tie stripes are competing with the stripes on your suit or your shirt and you have to make sure they don't create a visual cacophony - this should be readily apparent with a quick glance in a mirror.
Also remember that your eye is the final and decisive factor before you walk out the door. Rules of fashion can, and in some instances should, be broken...with the caveat that the result has to look GOOD. Likewise, the rules provided are general rules and if you adhere to them and still wind up thinking that something just doesn't look right, then it probably doesn't and you should change it.