Depending on the game, 300ms can work fine, but 1000 is really a bit too much.
With wifi when multiple devices are connected, some can gain priority over others depending on the applications and processes running on them. Even if they are not downloading/uploading files, but running something like an IM, it still can prevent you from accessing a portion of the available net speed. There are net speed boosters out there which basically helps you utilize the complete speed of your network that isn't actually being used by any other processes. I haven't tried these in a WiFi setup, but they might be able to help in your case.
With wifi when multiple devices are connected, some can gain priority over others depending on the applications and processes running on them. Even if they are not downloading/uploading files, but running something like an IM, it still can prevent you from accessing a portion of the available net speed. There are net speed boosters out there which basically helps you utilize the complete speed of your network that isn't actually being used by any other processes. I haven't tried these in a WiFi setup, but they might be able to help in your case.