For a 3 TH/s mining rig, you honestly do not need a powerful machine at all. Even back then, mining software itself was lightweight compared to the ASIC hardware doing the actual hashing.
If you’re mining in a pool, the setup becomes even simpler because the pool handles most of the blockchain work. In that case:
a lightweight Linux distro is enough
low-end CPU and RAM are fine
SSD storage is enough
bandwidth usage is actually pretty small with Stratum
A minimal Debian or Ubuntu Server install would probably be the best balance between simplicity and stability.
Minimum packages usually include things like:
build-essential
libcurl4-openssl-dev
libjansson-dev
libssl-dev
pkg-config
git
screen
Then install either CGMiner or BFGMiner depending on your hardware.
Bandwidth with Stratum is very low because miners mostly send shares and receive small work updates. Even slow home internet connections usually handle it fine. The old getblocktemplate method uses more bandwidth and more local processing because the node participates more directly with the blockchain.
If you run a full Bitcoin node (bitcoind), then storage, upload bandwidth, and validation requirements increase significantly because the node must sync and verify the blockchain.
