With your circumstances (internal graphics, 4GB RAM tops) I would consider using Raspberry PI 4 as a desktop computer (seriously, no sarcasm). If you are interested in reduced footprint, take a look at Lenovo ThinkCentre Tiny series: they have a VESA mount to hang behind the monitor and the price starts around $400 (your ITX case + PSU)
No quite enough CPU ;). It's getting a bit dated of course, but my machine is running a Devils Canyon 4790k (at stock speeds), 16G ram, 1.5TB of storage (NVME M2 and a 2.5" drive) and a rx5700.
