My question is simple. I am processing medium format 80 mp photos with photoshop and lightroom and when I go to get them printed at Walmart on their EPSON 7880 printer at 24 x36 inches, I do not care how much ink they use, I just want the best quality print. So what ppi do I set my editing at? 300, 600, 720, 1400, what?
To get the maximum quality you would usually send the native resolution. This will rarely be a nice and round number. This is because a printer can discard extra but it cannot make up for missing details. It also avoids double resampling since a printer has to convert to its inner resolution and resolution.
Say your 80 MP is 10328 x 7760 pixels, then a 36 x 24 print would have 286 PPI is you resize to fit (adding borders on two sides) or 323 PPI if you resize to fill (cropping as needed). Making up extra resolution will not help and may even add artifacts since the printer will resample a resampled file.
Most printers have a list of accepted filetypes, so I would check with them before choosing what to save your photos as. It depends what kind of paper you are printing on and how big the print is. For example, if you print on glossy photo paper, the standard is a bare minimum of 200dpi. If you print on newspaper, it's closer to 70dpi (the paper would just absorb all the ink of a 200dpi print and turn into one blurry mess).
There's also the factor of how big the print is. Usually with larger prints, people tend to stand further away, so you can get away with slightly lower resolution prints. If you're going to go 200 or under though, actually inspect your image. If it's a really high quality image, barely any grain, sharp focus, this will also help you to be able to settle for a lower dpi.
I believe the native resolution of that printer is 360. Since this is higher than what you can provide for the aforementioned print size, just send them the full resolution file. Your photo editor should calculate the actual ppi based on the target size.
Avoid lossy compression (JPEG).