Firstoff you will have to check the NYC laws to make certain that you are allowed to keep powder and primers in your home!
The simplest of presses are the single stage press. These you use to process cases in a batch of 20, 50 or 100. Size them, prep them, clean them, primer them, bell them (pistol), add powder and bullet, then crimp.
A progress or automatic press has 3, 4, or 5 stations and as the case moves through each station it does the sizing, priming, powder drop, bullet and crimping. You do have to pay attention to each operation.
You are best buying several reloading books and reading up on what you need. A basin kit is the best way to go. You need the case prep tools, a powder scale and a caliper.