Start here
Fish Supplies: Tropical Fish Tank and Aquarium Supplies look through their catalog. That will tell you how much $$ you will need.
A 50gal tank is an odd size so they are more expensive. Where a 55 gal is one of the most mass produced tanks there is. You can normally find a brand new tank (tank only) for not much more than $100 bucks. Or if you search around in your classifieds you can normally find tanks (55gals) with equipment and stand for about the same price. Mind you these are normally NOT Salt Water setups.
For equipment you are going to need.
Lighting: on a 55 gal with live rock you need 2 watts per gallon, so you need a fixture that is 110 watts minimum.
Protein skimmer
2 power heads rated at 350 gallons per hr (that is on the low side IMO)
Live rock: You will need to buy some to get started
Substrate: What kind you get is a matter of personal opinion.
Heater: in a 55 gal I prefer to have 2 smaller ones vs on large one.
Salt mix:
Hydrometer:
Thermomiter:
RO water: I would rather spend 80 bucks on an RO unit vs constantly buying RO water and having to lug it home.
Now with you wanting to grow your own live rock. Wile yes this will work, but in a FOWLR tank the live rock serves as your filter. Hence one not being on the list I gave you. However if you do not have enough live rock to properly filter your water then you will need an additional means of filtration ie a filter. Furthermore wile yes you can "grow" (don't know that I would really call it that) your own live rock, this take a lot of time. IMO it's better to just start out with all the live rock you need.