Another internal drive for sure. You only use external drives for portability, ie moving files between laptops at school. The size really depends on your budget, if you have the cash, get a 1TB drive as a game drive and fill that baby up with games. At the bare minimum, I say another 500GB (half of 1 TB). I suggest you read up on this article so you know the trade-offs between different storage standards and understand the different between the communication protocols (NVME vs SATA) and physical connector (SATA connector vs M.2).
Confused about different SSDs? We pit PCIe vs SATA SSD interfaces and also compare all the different SSDs like SATA 3, M.2, 2.5-inch and NVMe SSDs