I just started setup as well, getting back into the hobby. Regarding rock, a lot of the guidance you'll see out there is in terms of lbs per gallon. Looking at those guides, it's the same ratios now with people using man made rock which is extremely dense and heavy as live rock from the ocean which is very porous and relatively light. I'd consider all that sort of guidance as very questionable, and you'll really want to focus on the aquascape looking good and checking your levels to figure out what's actually right for you.
I like the man made or mined rock though. You can control what goes into your tank, and you're not destroying the reefs. With a 13 gallon you'll even more want control.
I used the Caribsea Liferock, mostly because it looked kind of natural and I got a major deal from PetSmart's site through doordash delivery. I also used Fritz turbo start I got per recommendation from Neptune aquatics. That all combined with dosing Ammonia and a ton of API ammonia measurements made the cycling pretty fast and straightforward. I would not buy live sand personally, since you're paying for water in the bag and the bottled bacteria certainly more live and not that expensive.
Also, set aside budget for a new pump or powerhead for the fluval. The stock pump is very weak.
Final suggestion, prioritize easy when buying things. Especially in a small tank, you need maintenance to be easy so that you stay on top of it and avoid things going south. Spend a couple extra dollars for the easy to use salinity testers, supplies for water changes, and so on. It's relatively cheap to do easy things like water changes in a tank like that, and that's a great way to control what's going on.
Have fun!
