What is the right way to float a home lab?

You can't float everything without an isolation transformer - the neutral will be connected to ground at the entry into the building. For safety any class I equipment does need to remain grounded, in my lab I have an isolation transformer only for the equipment under test, the scope and power supplies still have the case grounds, and are tolerant of the inputs/outputs floating up to 50V from ground (per their manuals). If I need to measure high side DC stuff, I can connect the high side to the scope ground (since the isolation transformer allows that offset) but a differential probe is still needed for measuring small signals with a large offset - it's far cheaper to buy one than smoke an oscilloscope

What is the right way to float my home lab?

If you want to make measurements that are isolated from ground, the only way to do this is with an isolation transformer if your scope is not isolated. There are very few reasons to do this, a high voltage setup would be one reason. Some AC measurements would be another. Differential probes are best.

Do I float my three devices separately? For example, somehow removing the ground from the socket coming from the device?

A reason to do this would for breaking a ground loop on the scope, so that is most likely the only piece of equipment that you'd need to do this on. If you are doing this for AC measurements, the scope could also be floated. It is unsafe to do this on power supplies, where will the fault current go? Not to ground.

There are better ways to eliminate ground loops, one being a differential probe (kind of pricey). Another would be minimizing the grounds between devices, and making sure they are not plugged in on different circuits or plugs. (I've had a few times where this was an issue)

Can I plug everything into a mains power strip and remove the ground of the mains power strip before plugging it into the wall?

No, also very unsafe. No path for a fault current.

There is no right way to float your home lab.

1) No. Right way is not to float equipment that must be grounded.

2) No. Don't float any of them. Equipment that have grounded plugs NEED to be grounded for a reason.

3) No. Because again, equipment with ground pins need to be grounded! Having all lab equipment and the device being examined being connected to single power strip at least makes them being powered from same mains phase and having a single point ground reference.