One of my dream vacations is to get my wife and kid Eurail Global Passes for a few weeks or a month, and just backpack everywhere constantly staying in hostels and seeing everything. It'd probably be kind of stressful and tiring, but memorable.
I've never done that, exactly, but I've done several trips of that length around Europe and South America.
My (general) sanity rules have become these: never stop for less than two nights, always spend four nights in the same place after 2-3 shorter stops, and spend a full week somewhere during the trip.
While this may feel limiting, I've found that anything more strenuous has always overwhelmed someone in the group.
I'd say: do the opposite! Don't plan anything, stay no more than two nights at the same place, jump on a train and see where you end up. Then, if you don't like, just take the next train somewhere else.
I did this twice in my early twenties and it was amazing. I mean, it was absolutely horrible. I slept on bark benches, in Cafés, in train stations, before train stations (until they turned on the sprinklers)... I was picked up by the police because we got lost in a field and more than once I was convinced I'd die. But it was absolutely worth it and both trips became core memories / PTSD trigger.
But seriously, don't follow this advice if you have a kid and are not an immortal twenty-something.
Thank you for the sane guidelines. My latent hubris would no doubt have me blurring about the continent like the subject of an international manhunt. Having spent 48 hours on a cross country Amtrak once, I should be less keen to recreate the experience in European terms.