I’m quite interested in trying to set up magento with the One-Click Application. However, I’d like to know a few details about that application before doing so such as
Is there some documentation with the specific server and software configuration somewhere? Thanks!
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so far i know, mostly all DO one-click application comes without any custom optimization. it installs the basic and you need to optimize as per your need.
there are plenty of optimization tips on tutorial section
How To Optimize Apache Web Server Performance
How To Optimize Queries and Tables in MySQL and MariaDB on a VPS
magento one-click comes with apache & ubuntu 14.04 but if you want my opinion i would suggest you to build with Nginx. nginx alone would give you much better performance over apache. also if you choose ubuntu 16.04 you would get php7 & mysql 5.7. both are proven to be much faster then older versions as well.
its not recommended to use one click appliciation for production use. its mainly available for development and test purpose only.