First off, congrats on the upgrade! 55G are great, I got one comin!! I'm assuming that the tank has been empty and without water for four years. If thats the case.....
1) Concerning the rocks....you can take them out and vigoursly wash them in a water/bleach solution....when you're done make sure you rinse, rinse, rinse and rinse again!!! Then let them air dry 100%
2) The crusty stuff might be calcium-deposits built up....the easiest way to clean them is just use a paper towel and water(atleast thats what I do) for the filter, you can disassemble it the best you can and soak them in hot water and rinse rinse rinse and let them air dry.
3) Do you know the name of your fiter? If it's a bio-wheel filter, and they've been sitting out for 4 years...without a doubt the bacteria is dead. You will need to get new ones. They are available at any of your LFS.
The best way to get your tank up and running is making sure you let it cycle.....a fishless cycle......you can read up on it with this link: Fishless Cycling Made Easy
It will take anywhere for 3-6 weeks to cycle. It's a very important process which will make your life and your fishes life a lot easier in the long run.
Do you have a subtrate to use? Make sure that gets in there before you fill your tank up!!
Any thoughts on the fish you wanna use yet?
Any more quesitons, feel free to fire away, the people on here are experts!