The more expensive the component is usually tells you that it is better and lighter. Try to save weight by buying the best components that you can comfortably afford. Remember to keep a few bucks in your pocket for gas and food.
This depends entirely on what troubles you are having. Upgrading your bike won't instantly make you a better rider. If you have a mid to top of the line bike you probably don't need to upgrade at all. If you bought a good entry level bike (Prominent manufacturer and price greater than say 500-600 for a hardtail 1200+ for full susp. $$)...
1. Seat (get something comfortable)
2. Tires (Get appropriate tires for your riding conditions. "Do it all" usually means "sucks at any one thing")
3. Wheels (Lighter/stronger and perhaps for tubless tires)
This should really help.... As your skill improves look into buying a new bike. If you can't do this piecing together your upgrades on a solid frame is an option. Drive train, brakes, etc.... You can tell if this will work for your frame if the higher end bikes your manufacturer makes feature the same frame and materials.
For example: a Trek 4300 frame is the same hardtail frame used on the 6 series bikes. The differences are the components.
Lastly, If you feel something holding you back... Braking, Power transfer, weight etc.