@StijnT this 
Agreed on the don’t buy a Pi part. You can get a used NUC or probably already have an old pc/laptop laying around which you can use.
Don’t agree with this monster’s @stevemann’s recommendation to go bare metal though 
There’s plenty of easy ways to make the most of a NUC’s extra power to run other stuff via Proxmox, most of which can be installed using a 1-line command using the awesome (RIP mate) tteck’s scripts.