So you would not connect the scope directly to mains, but put isolation transformer in between?
Which brand and type you would recommend? How expensive?
No, NEVER isolate or float the oscilloscope. If you want to use an isolation transformer isolate the device in which you want to measure. But be aware that an isolation transformer (or an isolated oscilloscope) reduces but not eliminates the risk.
If you need an isolated oscilloscope, get isolated probes (note: differential probes not necessarily mean they are isolated, check if they are), or get one of those special isolated oscilloscopes.
Also note that a battery operated oscilloscope is not necessarily properly insulated. E.g. blank BNC connectors are typically a sign that an oscilloscope is not. But non-blank connectors still don't mean it is properly isolated.