Can you provide the URL you got Forge from instead of "THE OFFICIAL FORGE WEBSITE", many have made their site look like the official in order to get you to download their BS and I've seen many people come here after being hoodwinked by these sites.
When it comes to crashes like this during lifecycle events you can look down the list and check fore the first one that hasn't completed the lifecycle step.
In this case it's BetterHUD, which sounds like a client-only mod because HUDs don't exist on the server
Click "New", and in the window that pops up:
Name is the Installations name
Version is the Minecraft (or in this case, Forge) version that gets used.
Game Directory is where the logs, saves, screenshots, mods, etc. folders are put.
The filenames of one or more of your mods suggests you got them from a repost site.
Please read up on the StopModReposts project (link in my signature) for info on why this is a bad thing.
You have at least one client-only mod on your server.
Am I understanding this correctly?
You're worried that one or more of the curses in this pack will stress your computer too much and might result in the loss/corruption of your savegame?
As you're using Twitch you're probably not getting the log that would provide the most information,
please follow the instructions in my signature (Logs Section, Twitch Launcher Sub-Section) to generate this log.