I looked into it as a family holiday when my DC were young teens (about 10 years ago) as I thought it would be a great experience for them to spend the summer travelling around Europe. We didn't do it because it is so much more expensive now and because sleeper trains aren't the most comfortable mode of travel...
I've taken quite a few sleeper trains in Europe, Africa and India with the luxury of a private cabin in recent years and it's fine as a one off but it's pretty exhausting and uncomfortable. When I went inter railing, we took a crazy route zigzagging between countries every few days to save on accommodation by taking overnight train rather than a logical route eg instead of Brussels. Bruges, Paris, Nice, we did Paris, Vienna, Nice, Berlin etc
I think if I spent a 2 week holiday doing that, I would need a 2 week holiday to recover.
It worked out cheaper to take budget flights if we weren't going to do the mad zigzag sleeper train route that saved on paying for a hostel/hotel. The tickets are much more expensive in real terms than they were when I was a teenager and they are limited on the number of trains you can take depending on and there are extra charges for night trains.
If you do decide to do it, you need to price out the different options. If you make a lot of short journeys, it might be cheaper to buy a country pass and fly or buy individual train tickets. If you are opting for a sleeper cabin (although some services have shared couchettes that are a lot cheaper), it may be cheaper to fly.
I wouldn't worry about living out of a rucksack or washing your undies in the bathroom sink with travel wash
A wheeled suitcase with 2 weeks' worth of clothes will be fine. Take a crease release spray if you don't want to look dishevelled. If you do want a rucksack, you can get great wheeled rucksacks with detachable day packs and zip up panels to put the straps away. I have an Osprey one, they have a good reputation. I've only ever used it as a rucksack when I've been in places where there are no roads/pavements though, that's not much of an issue in Europe.