My twocents as I piecemealed things together and dream of a 10 gallon automated system when I hit the lottery, here is my recommended order of purchase for 10 gallon batches:
-MILL!!! (I have Monster Mill and LOVE it.)
-15-20 gallon kettle
-Appropriate burner, LOVE my Blichmann for brewing in garage, don’t worry @sneezles61, electric 10 gal is in my near future
-PUMP (I do 5 gallon batches (for now ) and use a ladder to hold kettle to gravity drain through CFC, would NOT do this for 10 gal batches, lifting 6 gals of boiling liquid manually is sketchy enough )
-Chiller (Internal chiller is nice for whirlpool, I use CFC for most of my brews)
-used kegs (much cheaper, work just as well, may need some cleaning/seals/gaskets depending on where you source them)
-Kegerator (you may want to check craigslist for used fridge and build one, I bought mine from kegerator.com)
-Perlick faucets (preferably with flow control, it’s amazing, also, get Perlick’s, they’re worth every penny)
I Batch Sparge and use a propane burner so obviously you’d need a way to mash on top of this suggested list of equipment. Many on this forum would highly recommend BIAB, but I’ve never tried it. I get 75-80% efficiency with batch sparging and love it, thanks @denny!!.
This priority list also assumes you have vessels to ferment in, I don’t secondary, but have two 6.5 gal fermentors that I typically keep brews in for 2-3 weeks before transferring to kegs.