After a lot of research and deliberation, I went with an Arduino MKR 1010 board since it's got both WiFi and Bluetooth. I also got the MKRTHERM shield. I had been considering the breakout board the Adafruit sells that has the same controller on it (the MAX31855), but rather than have to have a messy breadboard for no reason, I figured the shield would work better. I *did* end up ordering the K-thermocouple from Adafruit as they had a decent one for $10. I think it goes up to 500F and I plan to use this for my smoker, so I wouldn't need it to go any higher than 375F and they tend to be more accurate in the middle of their range.
So that's pretty neat! Next step will be the get the board and flash it with the example code and test it against ambient temp, ice water, and boiling water. After that I'll probably work on the WiFi and server code. Then I'll worry about local display. Once all that is working correctly it'll be time to tackle the fan chunk of this project - which I think is probably going to be the hardest part. (Although I haven't done too much searching, maybe someone out there has some code I can use as a starting point) I'm pretty excited!