Honestly, if you are doing things so naughty (which I don't advocate) that you are worried about state adversaries using lots of resources to track you down, you probably need a level of OpSec that you are not likely to achieve without being supported by another state level espionage agency. But at the very least you should be disguising yourself (in such a way that you still blend in), you should not be accessing an AP within a few hundred miles of where you actually live, you should probably not be driving your personal vehicle anywhere near the AP you log into (instead, using public transport paid with cash and then sitting on a park bench near the AP), you should probably be using a computer you purchased second hand from a thrift store with cash at least 6 months ago, you should probably wear gloves, you should probably dispose of the computer in a public dumpster in a different town than you accessed the AP. Hell, you probably shouldn't even download TAILS from an IP you control, I have no doubt every Tor Bundle and TAILS and WHONIX download is logged for cross referencing. Even with all of that, I honestly doubt that in the current climate a normal, highly careful person could remain anonymous if they were targeted by a major western intelligence agency like the NSA or the GCHQ.
Obviously this means you are doing something illegal but undetected, like spying for the Russians or Chinese in the West, spying for the West in Russia or China, etc.
OTOH, if you are doing something like exposing human rights violations in China/Russia/Iran/etc. where, by its very nature, the results of your (in that place) illegal activity are published, you are far more likely to be targeted.
Which distro? One known problem is that browsers still transmit their location. If the network and the laptop are hundreds of yards distant, that's an instant red flag. Once that problem is corrected, there may be unknown problems to deal with.