Generally the connection itself is a foundation of online play.
Long ago I dailed a friend's number to play a game with him. Then dailup came. Pings were in the 350's and the framerates were about 4 per second at times. Back then servers for online play usually had a 400 or less limits to kick slower players out.
T1 was the speed to go then. Now it's obselete. I run fiber optic from DSL which itself is now obselete.
On fiber online play for me with the same hard ware has improved greatly. Connection to the server was 120 ping and now some dip into the 19 range.
Hardware counts. If your machine is beefy and can BE a server then you should be equal to or better than the actual server that is rented to the group hosting the online game.
Monitor needs to have a reaction time of 2ms or less. No wireless or satellite to net. Just fiber or wired is best for gaming.
There are times you encounter a server that is a computer loaded with several different online games to make extra money for the renting company and it's quite bad. You want a pure server that only plays one game. Nothing else.
Hardware is king, but is no good if you are not connected. Savvy? (Cue blazing saddles movie please)
One more thing.
Your Laser mouse with a very high adjustable DPI is one of the best upgrades you can do for gaming online.
Cranking the DPI very high allows you to spin a tank turret very fast across "The game world" or slowing the DPI way down reduces the impact of a sniper's scope and allow you to shoot either an eye or a ear. Not just squeeze and pray you get a kill message and not a got killed message.
Here is a tip.
If your player starts to play Ballet really fast spinning while you run around a corner, your DPI is too damn high.
At the end of the day when it all done online, I want to have a connection and a computer to BE the server, not to be trying to hope to finish a game with one.