The TC code in Marlin is based on having a MAX6675 (EOL'ed, now superseded by the MAX31855) or AnalogDevices AD595 IC connected - the type of thermocouple connected to it is then entirely based on what MAX31855 you have connected. I.e, its not designed to go through a lab-grade OpAmp and doing cold-junction conditioning - Marlin instead expects you to have an IC that does all that for you and simply spits out the corrected/calibrated tempreature upon request...
The bulk of MAX6675 or MAX31855 chips you find in "breakout board", will be the K-Type... And the AD595 is *only* good for K-types (the 594 does J-Types). The max-delta-T on each type of thermo couple chages, but for a K-Type, it hovers around the 1.5°C delta up to 400, and after 600 starts almost climbing in a log fashion (600 is 2.4, 800 is 3.2, 1000 is 4.0 etc).
E-Type is worse for the temp ranges concerned with printing, and a J-type is indentical in error curve of a K-Type but tops out at just over 600 anyway. If you wanted the lowest delta across the widest range, R or S are the ones to go for, with a max delta of 1.0°C across the most used temp ranges, and only starts log climbing above 1400°C. So - You can use 'any' Thermocouple, as long as you add the 'appropriate' MAX or AD594/595 circuit (I personally don't like the AD595's.. so would err to a MAX31855 myself...) .
If you do your own MAX31855 circuit, you can get the R or S type IC and use the respective TC's (bearing in mind R stands for "Rudely Expensive" and S for "Stupidly Expensive"....
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In terms of Thermistor vs Thermocouple - remember that a Thermistor is usually more accurate than a Thermocouple (depending on conditioning), and thermocouples are subject to high noise distortion due to their much smaller voltage. But thermocouples can do higher temps... from a 'reading' prespective a TC has a mostly linear response curve and can be interpolated but a Thermistor has a non-linear curve and needs map tables.... So its all a tradeoff really as to whats the best approach for the specific application.