I am looking to try to improve my 2005 trek 1000 and I had some questions about compatibility.

• If I change from a three ring to a two would it effect my shifters or are shifters designed for a certain gear number and ratio
  
• Are all 700c wheels compatible. If I get new wheels will my old cassette fit.
  
• When cleaning my rear cassette can I use bike degreaser or will it mess it up (If it does what should I use to clean it)
  
• I don't have alot of money but What would be the component that would make the most difference in performance? Wheels...crank...carbon bars, seatpost, or forks. I want to upgrade but I don't have the money to buy a new bike.

Going from 3 to 2 chainrings should be fine and not require a new derailleur or shifter. Note that double-chainring cranksets usually require a narrower bottom bracket than triples do.
Rear road hubs are either Shimano or Campagnolo-compatible. Many brands are available in both versions.
Degreaser and a stiff-bristled plastic brush work well on cassettes.
Wheels are rotating weight, so upgrading them will likely make the biggest difference. After them, I'd upgrade the forks.

Wheels,
Tires,
Pedals,
and watch for some near new 105 or Ultegra 8-speed shifters on ebay.

After that, it's not worth it. Wait until you can afford to buy a new bike and swap the wheels and pedals over.

Leave your drivetrain components alone. You can spend a lot of money and there's very little you can do that will improve them. That includes changing from a triple to a double; all you get is fewer gears.

+1, and add

Brake pads
Saddle (maybe)
Adjust the fit (possibly a different stem, find the best saddle position, etc.)
Shoes, chamois, gloves...



As Lance says, "It's not about the bike".