I have rehabilitated more than one C-Band dish, and I have never spent all that much money on any of them. I disagree with what another poster suggested about using one dish for Ku-band and C-band; in my experience that never works out well because one or the other will probably not be at quite the correct focal depth, due to the way dishes are designed. And if you ever decide to build yourself a satellite backend system using tuner cards with multiple inputs you will find it's nice to have more than a single dish.
Now people will disagree on certain points but mostly it depends on whether you are dead set on trying to rehabilitate older equipment or whether you want to use new equipment. IMHO it is more costly to rehabilitate the old stuff, except for the dish itself and maybe the positioner motor if it's not super old. If this is your only dish then I would guess you probably want it to be movable, whereas if you had multiple dishes you might find it advantageous to lock each one down on a single satellite, especially if you build a backend system using software such as TVHeadEnd.
So I am going to assume that you can use your current receiver, and that you want the dish to be movable, and that the positioner motor isn't super old (which would mean it probably has some kind of unique and funky control mechanism). The main thing you will probably want to get a new C-band LNB. If I were you I would get one with dual outputs even if you only have a single tuner, because the duals aren't that much more expensive and someday you may get a receiver with dual inputs, or build that backend system I keep mentioning. Also if you ever do something dumb and fry that LNB output, or if a power surge or lightning strike hits close enough to fry that output, the other might still work. Just be sure to cap the connector with a weatherproof cap of some kind until you need it.
The reason to get a new LNB is because most of the newer digital receivers, probably like the one you have, use voltage switching to change polarity whereas the older ones used a motor-driven mechanism that is not supported by the newer receivers. You can get a box that will convert the signals from your new receiver to your older LNB but you will pay way more than the cost of a new LNB, and depending on the age of the old one you will probably get better performance from the new LNB as well.
You will also need cable to connect the LNB to the receiver, I recommend RG-6 for shorter runs of about 100 feet or less, and RG-11 for longer runs. On marginal signals the amount of loss in the cable could make a huge difference. It is up to you if you want to run one or two cables out to the dish, but if you think you may ever want two it's usually easier to run both at the same time. Also, I always get a coil of the cheapest black plastic irrigation type I can get, you can get a roll of 100' of the 1" diameter stuff for about $20 give or take a little, and only a little more if you go larger diameter, and then bury that between your house and the dish, and then pull your cable(s) through that. The way I do it is to take a kite string and tie it to a small wad of cotton (I've also used tissue paper in a pinch) and stick that in one end of the pipe, then put a vacuum cleaner hose on the other end and turn on the vacuum while feeding the kite string until the wad of material appears. Then I tie and tape the string to the cable and use that to pull the cable back through. You will thank yourself for doing this if you ever have to replace the cable, or if you are ever digging for some other reason and forget exactly where that cable is and hit the irrigation pipe instead of cutting the cable. Also don't forget a tube of silicone caulk to seal the ends of the pipe against rain.
I'm assuming you have the pole that the dish goes on and it is already set in the ground, but if not then don't forget that you need a pole and concrete to set it (I only use about 3 to 4 bags, some people use less and some use a lot more, particularly in hurricane-prone areas). People will do all kinds of crazy things to keep the pole from twisting in the concrete, but I've never had one turn in the ground on me after the concrete was set and at most all I've ever done was give the end that will go in the concrete a few good hard whacks with a sledge hammer to deform it a little. Then again I am NOT in an area that gets a lot of heavy winds, although we've had a few good storms here. If I lived in an area that gets hurricanes I'm sure I'd do some crazy things to keep the pole from turning in the concrete too. The main thing to remember when setting the pole is it must be PERFECTLY vertical - check it with a level on several sides before the concrete sets and make adjustments if necessary. And also don't get a pole so short that the dish will touch the ground when you swing it to the far east or west (personal experience talking here). If you have run the plastic pipe I mentioned in the previous paragraph, tape it to the pole in the position you want it before pouring the concrete so that the bottom will be in the concrete, this helps protect it from lawnmowers and weed-whackers that might otherwise be used too close to the pipe. If you need a pole and have a recycling (scrap metal) yard in your area check there, often they will have some used well casing pipe of the correct diameter, it may be rusty but a little work with a wire brush and/or sandpaper and a coating of Rust-Oleum Rust Reformer followed by a top coat of black spray paint will make it look presentable.
Then there is the positioner motor. If the positioner you have isn't from the dawn of time then chances are it will take a four wire cable. Two wires feed voltage to the motor and should be fairly hefty (I would say #18 minimum, probably #16 would be better and some will even recommend #14, but for long runs you will want even larger) but the other two are just sensor wires and can be smaller, like #20 or #22, though the don't have to be. They deliver pulses from a reed sensor or some other kind of sensor mechanism that sends pulses as the dish moves. I haven't ever had to buy this type of cable, I got a hunk with my first dish that I still use on my one moveable dish, so if anyone else has a recommendation for that type of cable take a look at what they recommend.
Then inside you will need a control box of some kind. I use a V-box which can be controlled with DiSEqC signals from a compatible receiver, but since my only moveable dish mostly says parked in one spot and I only move it if I'm trying to verify what's on another satellite, I just use the remote control to move it. Some people don't like the V-box for various reasons and recommend other solutions, but I've never had any problems with mine (then again I unplug it whenever I'm not actually wanting to move the dish). So I am a little out of my depth when it comes to positioners and controllers, because I move my dish so seldom, but basically that is what you need if you want the dish to be moveable.
And finally, if you want to use your current receiver to receive signals from both of your dishes, and you don't have dual tuner inputs on your receiver (which is pretty rare), you will need a switch of some kind. With only two dishes and one receiver you could use a 22 kHz tone switch, assuming your receiver supports it, or a multi-input DiSEqC switch of whatever type your receiver supports. I'm guessing your receiver will probably support any modern DiSEqC switch and/or a 22 kHz tone switch, but I don't know for sure since I don't own one. Switches can be finicky so I recommend you get one from a trusted dealer in case the first one you get is defective.
Now as I say I am sure some people may disagree with some of what I have said (especially the people who are obsessive about welding all types of stuff onto a pole to make ABSOLUTELY CERTAIN it will never twist in the concrete) but hopefully I have covered the basics. You're probably familiar with most of the concepts already, it's pretty much just like Ku except you are dealing with a much larger dish. What I have not covered here are the basics of aiming the dish, because you don't seem to be at that point yet, and there are other posts that explain that.