Would this be a decent budget system for Premiere Pro

What Peru Bob stated is also very true. You see, by default Windows 10 and its default page file eat up well over half of that SSD's available space, leaving you with woefully insufficient room remaining to install many of the Creative Cloud programs. As configured, it has less than 20 GB of free space remaining on the primary SSD.

And you will not be able to add more than one additional SATA SSD to that system and still run at the disk's maximum speed. (I do not count the 1 TB HDD as no HDD of its era could sustain even 150 MB/s on the outer tracks.) That is because on the Z77 and H77 chipsets, only two of its six SATA ports run at even SATA 6.0 Gbps (600 MB/s) bandwidth; the other four only run at half that bandwidth, or SATA 3.0 Gbps (300 MB/s). Having all six SATA ports run at their full SATA 6.0 Gbps bandwidth would not come until the 4th-Gen (Haswell) Intel CPUs and the 8-series chipsets. And the 7-series chipsets and earlier do not officially support m.2 SSDs or NVMe.

...and the SSD is too small.

That system is too old for any newer version of Premiere Pro, and the last version that was compatible is now no longer available any more. Newer versions of Premiere Pro now require that all of the major hardware components of a system be no more than about four years old. Unfortunately, all third-gen Intel CPUs and all Radeon HD 7000 series GPUs are now over eight years old. So, expect abysmally slow performance, and potential frequent crashes, when running any currently available version of Premiere Pro.