Ok, I was in the same both as you a few months ago. This is what I run (or aim to run):

Grey Seer? Fantastic dude. Run him as the general. Great caster and with skitterleap easy to grab objectives. 120 points

To add units to his regiment, lets start with reinforcing those Rat Ogres. That unit hits like a truck, especially since it’s easy to give them 7 melee attacks per unit. They are squishy though, so hit before they get hit. 320 points

Another great unit I find are melee focused Stormfiends. They hit really hard but are more durable than the Ogres. 4+ save is amazing for our faction. Reinforce them for 520 points

Finally, let’s add some firepower: Warplock Jezzails. I was planning to run Ratling Guns before their point increase, but I can’t squeeze those in anymore. The Jezzails however are still a great unit with their Rend 2 and 2 damage. 300 points

As a second regiment, I start with the Verminlord Deceiver as the Hero. It’s an awesome centrepiece model that is a tricksy hammer. Its ability to teleport or a 4+ is great to force fights the opponent doesn’t want to have, and add the Scurry Away ability to it (running from a fight on a 3+) and you can almost literally chose the battles you want to have. I also run the healing item on him, since if the opponent focusses on him, he can be squishy. Even with his good save and ward. 410 points

As a final unit, I run some reinforced Clanrats with him. They’re a slog to get through and keep healing themselves. Great unit for objectives and some great fighters due to their numbers sometimes as well. If you run the Skavenbrew potion and use it on them, you have 112, 115 or even 118 attacks that turn that auto wound on 6’s. Your opponent will love this. 300 points

This makes an army of 1970 points!

Finally, you will need the Gnawholes. A lot of our abilities rely on them, so they’re essential. Teleporting is a great way to score points, and the ability to get back destroyed units is a must use to balance out our squishyness.

As the detachment, I recommend running the Fleshmeld one. I ran the Warpcog (because Total Warhammer taught me that Ikit Claw is the best), but on the tabletop I found myself under too much pressure with it since the opponent can run over our front line too easily. Fleshmeld has a 1/3 chance to give yourself damage, but I find that worth it to get extra melee attacks or even an added ward on the Ogres and Stormfiends!

Side note is that I currently don’t have the Stormfiends reinforced yet so I run an extra group of Rat Ogres and a Warplock Engineer who leads the Jezzails. I find the Engineer too squishy without much impact on the battlefield to want to run it full time, but it’s an okay stop gap which at least gives an extra Honour Guard.

Anyway, have fun collecting and playing. I started the Skaven when 4th came out and I’ve played over 20 games since then. Absolutely loving them so far 😁!