First game! Awesome game to pick! Derbys are special so I’m sure you’ll love it no matter the outcome.
I travel up from London. Trains out of London are usually reliable. Use a web app called Trainline or National Rail to check the latest running status and platform number. So if you’re up for such a early start, go for it. You’ll arrive around 830am, I think so plenty of time as you say. You’ll have a reserved seat so no stress. Get some breakfast and a coffee to take onto the train from maybe Pret or M&S food at the train station. The train food is average and over priced.
Once in Liverpool Lime you’ll have time to have a quick look around the town centre I’d say, before getting the shuttle bus for the fans up to Goodison from outside lime street station. Lots of people catch it so you’ll see it.
I’d personally also take a look at the park to see how close the ground is to Anfield and enjoy the walk down with the fans to the ground. The club shop is worth a visit too. Some people like to get into the ground an hour before to see the warm ups.
Hope this helps!
Have a great day!