If you´ve created a game (in this case a strategy game). How can you make it a normal browser game. That means, even if the user is logged out, some actions should continue. So the building-time, or the research time should continue after the user is logged out. The basics of a browser game.
server side, meaning your game is running on a server and the clients gets vital information from server (if you start a building construction the server send to client the progress of building);
client side, meaning if you close the game, at reopening the game recalculate new stats for game elements based on the time passed between last save and current time;
For a server side solution yes. PHP is one of the most used scripting languages, but… be aware that webservers don’t push data to clients. Which means they only send data if you request them. And they dont run a loop, calculating your game status each frame.