As NES games appear to be your priority, why not just buy one of the RS-8A units?
The issue is that I'm particular about the games I want.
I like Tetris, Tiger-Heli, Jackal, Tempest, Gyruss, Galaga, Galaxian, Gun.Smoke, etc.
I prefer the arcade versions of those, but most (except Tempest) were ported to the NES and those would play okay.
But the RS-8A has 250 (likely 30 repeated 8 times) built-in games
http://www.banggood.com/Coolboy-RS-8A-260-In-1-Portable-Handheld-Game-Console-Built-In-Battery-Support-TV-out-Toy-Gift-p-1053684.html, no way to add games, and only has Galaga from my list.
Fortunately, @Jeremymtc was kind enough to offer me his Dingoo A320, and as he pointed out, I expect it to be about perfect for what I want, i.e. it is small - about the size of the NES Famicon controller, it has good quality buttons and controls, has great battery life, it plays MAME games and many of the games I like were ONLY ported to MAME, and the others I prefer the MAME ports. Big thanks to Jeremymtc.
If that wasn't available, I most likely would have gone with something like this:
http://www.ebay.com/itm/8GB-4-3-32Bit-10000-Games-Built-In-Portable-Handheld-Video-Game-Console-Player-/252774524582?var=&hash=item3ada8926a6:m:mZ3GfHANAoWGmCT9a5CYWJw - it should allow me to add 20-30 NES games that I like. Drawbacks are possible bad D-pad controls, and possible battery life in storage issues.
My decision is over, but I'll follow the thread for a little bit in case anyone else is considering the same questions.