welcome to DO,
I'm here the same as you new to these stuff... :)
I just moved from the horrifying shared hosting companies that were stealing our money for bad services.
as I understand you want to know what to go for, and this is exactly what I want to ask few months ago...
I can say that Nginx is good compared to Apache for sure. There is a good combination you can go for: Nginx + Php-fpm (php5.5.8 latest ver) + mod_pagespeed. I guess it is better to get at least 1 GB RAM since is good to hold things up. I believe the majority is used Ubuntu for OS, but me I use Debian 7 64x And that is for the performance.
For security sake, I guess it is a long road and I'm still trying things out. You can go with SSH first and how to protect it. Then use Fail2Ban to protect whole system, and you got to be careful to create an image for your droplet whenever things are setup correctly before starting to testing things out. Mod_secuirty is also an excellent tool to protect your system " I heard coders say", but still didn't manage to make it work totally.
don't use memcached or xcache since they are nothing compared to mod_pagespeed. I'm not sure about Mysql compared to MariaDB... still not yet for me... testing soon.
for mail, I go with external service such as Zoho mail since they have free plan. I will go soon on paid one which is about $25 with extra features.
I can't say more because that really depends on you and what you are going to use applications and tools for.