Answer Description

A hybrid drive will meet these requirements, it is more affordable than an SSD and quicker than a HDD. A tape drive is more of a backup tool, and is slow, not ideal for regular use as described.

Wikipedia

In computing, a hybrid drive (solid state hybrid drive – SSHD) is a logical or physical storage device that combines a faster storage medium such as solid-state drive (SSD) with a higher-capacity hard disk drive (HDD). The intent is adding some of the speed of SSDs to the cost-effective storage capacity of traditional HDDs. The purpose of the SSD in a hybrid drive is to act as a cache for the data stored on the HDD, improving the overall performance by keeping copies of the most frequently used data on the faster SSD drive. There are two main configurations for implementing hybrid drives: dual-drive hybrid systems and solid-state hybrid drives. In dual-drive hybrid systems, physically separate SSD and HDD devices are installed in the same computer, having the data placement optimization performed either manually by the end user, or automatically by the operating system through the creation of a "hybrid" logical device. In solid-state hybrid drives, SSD and HDD functionalities are built into a single piece of hardware, where data placement optimization is performed either entirely by the device (self-optimized mode), or through placement "hints" supplied by the operating system (host-hinted mode).