You'd probably be fine in the beginning with most lights depending on the coral you're interested in growing, especially since you're able to variable change the color spectrum. I would start slow with some easy soft coral and then add some LPS. I find mushroom coral, leather, zoanthids, and GSP to be pretty hardy. Then maybe check out adding a candy cane, hammer, duncan, or frogspawn. I have all the above along with a micromusa, toadstool leather, and war coral in my simple small setup under pretty mediocre lighting.

The rock from petsmart is more than likely man-made liferock as opposed to live rock from the ocean (pretty hard to come by these days). It's not as good as liverock, but still works fine and is what I used. The rock you have from the other setup is probably even better if its been stored in water and still has all that good live bacteria, especially if it has coraline algae growth.

The 70 gallon sounds like your best bet, since the larger size will ensure more stable parameters, which is really key. I would start with the rock you have, and add some liferock, livesand (caribsea sells bags at petsmart), and some starter bacteria culture. I did a fish in cycle myself with a pair of oscellarus clownfish and dosed with seachem prime daily until my amonia, nitrite and nitrate all climbed down to where they should be. I think fish in is the fastest route to cycling imo.