Cured live rock is ready to go, no cycle (or little), add to your water and add fish/coral/etc. The downside is it costs more and may have undesirable issues (aiptasia/bad crabs/etc). Dry rock, or uncured live rock, will need a month or two being cured before it is ready to go.
I recommended existing live rock due to the ready to go method. If you are willing to wait, dry rock is really the best way because there are no undesirables. Curing it involves having a place to keep it and waiting. Mix up salt water, place rock in, circulate the water. Adding something (a uncooked shrimp, pure ammonia, something like BioSpira) to get the cycle started will help.
Yes, you can use tap water. RODI is ideal, IMO, especially with a smaller tank. I started my 58 and then 75 with RODI, and used nothing but in them. My 215 was started with tap water, and currently using tap water, due to needing such a large amount. Yes, add water, add salt, let mix, get to correct salinity, add sand/rock, and let it cycle/sit and mature.
Waiting for the maturity is the hardest part. When I started my 58 I used live rock from a tank being taken down and let it sit about 2 months. I ran a skimmer, did water changes and just watched all the life on the rock. I then added fish and lost the first few I added. IMO, the best practice would be nothing but live rock and clean up crew for 6 months.
Sand is personal preference although you can find proponents of shallow sand bed, deep sand bed, and bare bottom. They all have merits but in the end comes down to how you want it to look. Your livestock choices will impact this too. (You don't want sand sifting starfish in a bare bottom tank. Or jawfish.)