https://www.amazon.com/dp/B00KM6ZA9I/
The most reliable programmer I've used, an AVRISP MKII clone. USBasps are junk because they're so cheap, it's a lottery whether the one you get works correctly.
No Mouser cart that I know of. Takes all the fun out of it anyways.
https://mutable-instruments.net/archive/ambika/build/mobo/ is where I got all of my info from.
Flashed the processors with this - https://www.amazon.com/gp/product/B00KM6ZA9I There's a decent guide on the entire process on the mutable site. It's not the easiest thing to get done, but if you go slow and follow the directions you'll get it working.
With JLCPCB, you just upload a zip of the gerber files from Eagle. Lots of good Eagle tutorials on youtube. Once the zip is uploaded, you are pretty much done. You can choose a color for the mask, but the standard settings should be fine. I would suggest shipping via DHL. Nice and fast. Probably worth your time to look into other printing options too - PCBWay, Oshpark, and probably more are all good choices. The whole process feels a little scary at first, but it really is as easy it seems.
Amazon gave me the gift of delivery to the absolutely wrong house today, so I took it as a sign and upgraded to this https://www.amazon.com/gp/product/B00KM6ZA9I
Reviews say that Atmel Studio plays extremely well with it so that raises my confidence a bit. Was looking forward to getting started tonight, but I've still got 3 voice cards to solder, so I suppose I can wait.