I'm not an expert on this... I followed the complete how-to on a clean debian box (8 XEON cores, 16Gb RAM). When i look at my server, it's load is around 0.2, and about 2,5 Gb memory was used... So i guess you can run an electrum server on a VPS, given that you have some swap space. Altough, during the loading fase where you install bitcoind and load the blockchain, a sufficient amount of processing power and ram might speed things up

Totally agree with mocacinno. I am running an Electrum Server for Bitcoin and Litecoin on the same VPS. The processing power and ram is crucial during the Bitcoin "catching up" phase (synching to the blockchain, AND later creating the UTXOs for Electrum). SSD is essential during the catching up phase - I have tried with rotational HardDisks (7200RPM) and it is not possible for Bitcoin anymore (Litecoin, still possible). With rotational drives, the new blocks come in faster than the HD/CPU can process.
You will need 70GB of storage for the Bitcoin blockchain and 30 GB for the Electrum UTXOs, plus your Linux operating system, and dependancies requirement: I suggest a minimum of 150GB SSD.
Litecoin needs 10GB for its blockchain and 5 GB for the Electrum UTXOs.
When all are in synch, the VPS uses about 5GB of RAM and 10% CPU (total, including system, bitcoind, litecoind, electrum-servers).
Summary: I use a 4 CPUs core VPS with 8GB ram, and 150GB SSD storage, and run both Litecoin and Bitcoin Electrum-servers on the same VPS.
Thank you so much for the details , but do you ahve any idea about that "Console" tab on the Electrum Interface ? is it made by the owners of the servers ? If it's the case then how come Quickseller (as you can see his above post) changed the server but the console message didn't change .