You can run both. Start running it as a bitcoin node. You can choose either core or knots. You can add lightning later if you want.
I was lucky and got a used m710 under 50β¬ but had to flash the bios. I guess a fully operational one would cost you about 100β¬. I would go at least woth an i5. Ram can be upgraded later.
2TB ssd about 200β¬ new. So you should be able to build it for about 300β¬ total. Maybe less if you find another mini pc. HP has also a good series called prodesk or elitedesk