Looks great!
First thing you should do is get some good test kits. I prefer Salifert. They are easy to use and very reliable and accurate.
Second, you said you're using tap water. Do you have copper pipes? Are you on a well or are you on city water? If you have copper, you might want to also get a copper test kit and just verify that you don't have copper in the water. Copper is deadly to inverts, including corals since they are classified as inverts.
After you get your RO/DI unit up and running, I'd be doing some massive water changes over the course of the next month or so. If you're going to add more LR, now would be the perfect time to do so. This way you get the cycling done all at once. Then the fun begins.
It does sound like the start of a FANTASTIC system! Reef keeping will teach you patience like nothing else ever could.
