It is turn-based tactic/strategy 2D game with quite low data packets to send, even 300bps modem transfer would be sufficient for 2 players only. Any latency under 1s is tolerant. For more than 2 people let assume just to multiply needed transfter, thus for 1MB/s banwidth that is about 7000 people online max., which is more than I belive ever will be reached.
Thus required resources are quite low for nowadays standards.
For me, it looks like you can use websocket. It offers bi-directional communication and it uses well-known http port for initial handshake.
If you want to send preformatted packets around, and can cope with handling retries yourself, consider UDP.
In real-time game, losing few packets of players positions data will not be a big deal as it will be overwritten with new data anyway. So real time game with UDP does not bother to try to resend lost packets.