I own a 2007 Giant Rincon mountain bike. I am not a bike expert, what is the most important part of the bike and why? Also, does upgrading a fork really make a big difference in the way a bike rides?
The easiest parts to upgrade are the saddle and the pedals. These are perhaps the two most disputed and personal parts of a bike, and the easiest to replace. That is of course assuming you are happy with your drivetrain and at least reasonably happy with your fork (which can be quite expensive to get what you want). Once you find a favorite saddle, you'll want to put it on all your bikes. Same with pedals. The good news is, you'll be able to transfer both to any other bikes you may upgrade to (keep the originals for resale). A good suspension fork will make handling, especially downhill, much better. Ask local riders for their preferences, and why. Hope this helps.
I agree with rudymike about saddle and pedals as the first stop. Once you are happy with your choices there I would look at anything with bearings starting with the wheel hubs. The better the quality of hubs and/or the better the maintenance, the less rolling resistance, the more of your effort goes into making you go fast, less gets wasted. Same goes for the bottom bracket. If they are good quality, have they been overhauled since the bike was made in 2007? As this is a Mt bike do you have sealed bearing and what quality are they? Another reason I put emphasis on bearings is they are out of sight and usually out of mind, yet are critical for top notch function and fun. You can see your drive train and brakes but not your hub bearings. Remember grease doesn't make your hub turn faster, uncontaminated bearings and bearing races do, grease is a barrier to keep contaminants out first, a lube second.