Real time, over mobile networks, is a real problem. People in un-crowded areas served by 4G will do pretty well (up to a few hundred ms latency.) People in crowded cells (popular places/cities, and so forth) or on slower networks (HSPA, 3G, etc) will have more lag.
For a fighting game, you might want to read up on the GGPO architecture; they use a rewind-and-re-simulate mechanism, and hide latency with wind-up animations, to make "street fighter" type games work OK even over medium latency connections.
I would recommend against using WebSockets, and socket.io. The reason is that TCP suffers when there are packet drops; a single packet drop means that all the data that comes after must wait for a re-send before the receiving end will actually deliver the data -- it'll sit waiting in the kernel for the earlier data to be re-sent, because of the in-order guarantee. For low-latency games, UDP is a better choice.
"how do I game server" is a slightly too large subject to write about in a single forum thread, though. There's matchmaking, basic packet framing, basic socket usage, NAT traversal, latency compensation, metrics and statistics, performance tuning, hosting, and so much more...
