Got this up and running last night. Here are my notes:

On AWS EC2 micro instance for PCI compliance, reliability, and practice with AWS. Would probably work just as well on Digital Ocean or Vultr.

Used Debian 8 64 bit HVM AMI to get things started, with SSH access from a specific IP and open ports 80 + 443.

Total list of software installed via apt-get:
nginx
php5-fpm
mariadb-client
mariadb-server
php5-mysql
curl
php5-curl
sendmail

I used Nginx's WordPress config as starting point. Had to modify the PHP socket to match the listen directive in /etc/php5/fpm/pool.d/www.conf, but otherwise worked great.

Once I stopped getting 502 errors and loaded up the install files, things looked pretty good until I got to the license verification step. It said to put in the email address I bought the license with, but gave an error saying it wasn't recognized. I ended up forwarding my purchase receipt to the developer along with my error - this was around 11pm Tuesday evening. I went to bed, and by the time I had woken up I had two emails from the developer: one suggesting a possible fix on my end, and one indicating he had dug deeper on the problem - he found something on his end of things that might have been causing the error and would be working on fixing it today. I was pretty impressed with the quick response!

My hypothesis is that my .co email address was throwing some errors for the verification system but I have no real way of knowing for sure. Yet another reason why I'm moving away from a .co domain, as I've run into a couple of weird snags like this before... Either way, I tried it again last night and it succeeded. It's all hooked up to Stripe and, outside of setting up HTTPS for payments, seems ready to go!

A couple of hiccups along the way:

I didn't realize you needed to install php5-curl as well as php5-mysql at first, leading me to spend some time vehemently disagreeing with the install requirements page saying I didn't have cURL installed on the server. 502 Bad Gateway errors for the nginx WordPress config's PHP socket... I had to hunt down the location of the PHP5-FPM socket to fix this. Part of the installation includes setting 777 permissions on a few folders - I am going to experiment with setting those back down to something less worrisome and see if it breaks the installation tonight.