Yikes, that's a mess. That radiator and heater core need to be professionally flushed out of chassis or replaced. The amount of sediment in it is going to require many flushes to get most, repeat most, of it removed. Then comes the engine. You should pull the block plugs (SBC on each side, one just in front of starter and other just in front of oil filter) and run it with a hose stuffed in the radiator with the thermostat removed and heater core bypassed. This will create a hell of a mess as that gunk will be gushing from the block for the better part of an hour of run time. You need to keep track of the coolant temp during this process so as to not overheat the motor and make sure you're maintaining water in the radiator via hose flow volume.
This a heck of a process, but you have a heck of a mess there. Once you feel that what is coming out of the block drains is clean enough, then use the 2 part cleaner as Bonnewagon described. Once the flushing is complete fill it with an extended life coolant and expect to drain and flush it with new fluid at least one more time after some drive time.
Of course you'll need new thermostat and gasket, but all flushing needs to be done with the t-stat removed because it acts as a giant restrictor in the coolant system (which it's supposed to do during normal operation.)