|"I want to get a new SATA to add some more memory"|
Adding another HDD doesn't increase memory, it increases storage space.
"What would be the best choice for me as a new hard drive (size [at least 500GB] , manufacturer, type, etc.)?"
Size is really up to you. The larger the drive, the more you'll probably store on it. To me, that means more data is at risk if the drive were to fail. Make sure you have a backup plan in place. As for brand, Seagate is probably the most popular right now, followed by Western Digital. Look for SATA 3.0Gb/s, 7200 RPM, at least 16MB Cache. And check the warranty. Some only offer 1 yr, some offer 3 yrs, others offer 5 yrs.