Don't be quick to blame Discord itself or your internet - often the problem is that the app is hogging too many resources. Open Task Manager (or the equivalent on macOS) and check how much memory Discord is using while you're using it. If the number is through the roof, that's your culprit. Try disabling hardware acceleration in the app settings - go to User Settings, then Voice & Video, and look for the accelerated graphics option there. For a lot of people this helps when the graphics processor is conflicting with the system.
Also check how many extensions and bots are connected to the servers you're on. If there are a lot of them, they can put a strain on your connection and Discord itself. Disable the ones you're not actively using. And check for updates - sometimes a new version of the app conflicts with your operating system, especially if your Windows or macOS hasn't been updated in a while.
If none of that helps, then yeah, that's when you should check your actual network - but leave that for last, after you've ruled everything else out.