Sounds like a good scheme Penejane, I think a lot of us gradually accumulate stuff unnoticed! :lol:
Live rock, is as you correctly surmised, simply dead rock, which has been left in water for long enough for it to get full of bacteria to do the filtration.
If your LFS will sell you rock that is already "live", so much the easier. However if you get dry rock, which will sometimes be cheaper, you simply make it live by leaving it in salt water for normally 6 weeks. Easiest way is to put it in your tank, some flow via a powerhaed or two is needed, and then around 6 weeks later it is done, or as they say, "cycled". You test the water along the way to see how it's going. First couple of weeks the water will contain ammonia, then as this gets eaten it will contain nitrite. In around 6 weeks the nitrite will drop to zero as the bacteria that eat it get up to strength, and you are ready to go. In view of budget, an ammonia test kit is not essential, just a nitrite one so you can determine when the rock is finished & ready for fish. You may know a friendly reefer who could loan you a nitrite kit to do a few tests.
The correct order to set up the tank is to put together the tank, water, heater, rock & powerheads. Once the rock is cycled lighting & livestock can be added.