I went with a noname Chinese Android phone and I'm quite happy with my choice.
Just look for some reviews and verify that the phone is physically ok (doesn't rattle, the back closes ok without gaps etc).
The latest Chinese phones are usually based on the MT6589 chipset, with at least 1Gb of RAM and pretty decent internal storage; also most of them support an additional micro SD card and usually dual SIM (if you need that feature).
The processing power is normally more than enough. You don't have the best GPU, but if you don't play 3d shooters it should be ok (for example, I play Anomaly Warzone Earth on my phone and it's more than decent; also it doesn't heat that much as my previous Note).
The pros are that it's much cheaper (usually 1/2...1/3 of a Samsung phone).
The cons are that you probably should forget about service (you usually have a period when you can ask for another device if the one you receive is DOA), but that would happen with new Samsung devices anyway if you flash your own ROM.
Also software upgrades might be an issue (e.g. I don't know if they will ever make one), but if you're into flashing your custom ROMs you'll probably search for an unofficial ROM anyway. On the other hand, Samsung isn't that fast at pushing updates either.