Best option will be Moto X first Generation 32GB Model. Both screen size and RAM fits your requirement but its available on ebay.com at the price you are looking for.
I am going to root the device, so need good custom ROMs support. Pure android OS unlike what zenfone 2 and redmi note gives. 5.5" would be tough to fit in pocket while riding a bike i guess. How about LG G2 from ebay.com if I can get it from US for less than 250$, would it be a good deal against...
How about HTC Rhyme? Ain't it worth it at 18.5k, now?
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I am also looking for a phone in this range with secondary camera to be able to video chat or for video calls!