Planning an iOS release in the future but for now I'm perfecting the Android version. If you really want it you can pick up a low-cost Moto E or similar: https://www.amazon.com/Motorola-16GB-Unlocked-Quad-Core-Smartphone/dp/B00GWR373M/ref=pd_lpo_107_tr_t_3?_encoding=UTF8&psc=1&refRID=ZGR2TFPZFSXP6314KT93
I have a couple of these around my home with the App loaded on it for guests.
I have a Moto G. It's unlocked so it would work with T-Mobile. Not terribly expensive either. I love it, but I wish it had a bigger screen.
Don't download a ton of apps that are supposed to "optimize" your device. That's like eating a ton of snacks that are supposed to help you lose weight: you're gonna get fatter. Keep Greenify, forget the rest.
THIS is the best optimization: download apps you ARE going to use and delete everything else.
About CM... Do you know anything about rooting? Custom recovery? Bootloaders? Custom ROMs? I see you quite interested about the benefits of using CyanogenMod, but keep in mind that if you mess up during the process, you can brick your phone, lose it forever (I think you'd have to be pretty clumsy for this to happen, though).
Games: Duet, Mountain Valley, The Room (1 and 2), Leo's Fortune, Two Dots, Rayman Jungle / Fiesta Run, MyBoy! (Game Boy Advanced emulator; you can download the roms from the internet).
You have to remember this, though: games will drain your battery, no matter how good your phone is.
For a person that seems so enthused about the whole smartphone thing, I think you should really think about saving some money and buy a good phone. Some off-contract options:
OnePlus One: $300 (if you can get an invite)
And if you ever go to China, Meizu MX4 or Xiaomi Mi4.
Personally, I think if you live in the US the HTC is the best option.
Don't get a Samsung is my advice, awful phones to use. Get this instead: http://www.amazon.com/Motorola-Moto-Global-Unlocked-Black/dp/B00GWR373M/ref=sr_1_2?ie=UTF8&qid=1428396991&sr=8-2&keywords=moto+g
On the Amazon page some answers say that this won't work with Verizon.
Also, after doing some research I've been digging the 5"+ screens like on the Note 2 and LG G2. I like the phablet style. Are those two my best options at the moment for the screen size? No doubt the Moto G is newer, if it would work with Verizon.