Like Pako, I think the SEL 50 f1.8 when available will be the lens to take for this task (price, weight, size, stabilized, fully supported by NEX system : AF, aperture, ...).
In the manual focus world (lens I own or tried/test on the Sony NEX):
So far the best lens I use was the 58mm 1.2. In good condition, this lens is very good even wide open on the Sony NEX 5 (thanks to the manual focus zoom function -> but little bit hard when kid are running in the house ...). (~600$ on Ebay, too expensive if you don't have it always on your camera ...).
50mm 1.2 MD sharper than 58mm , but little less kindly out of focus effect (but almost half the size and weight) (~500$ on Ebay). more flare resistant than the 58mm.
58mm 1.4 MD last version is a very good lens too (~100$ on Ebay now).
50mm 1.4 MD last version is very good, I have gave the lens for a friend to play with and until now very satisfy. (~80$ on Ebay now).
With the MD-NEX adapter, those three last lens are comfortable and the weight is mostly in the lens, the Sony Nex become almost absent in the weight balance.
In the search for the perfect small portrait lens, you can go in the Leica mount:
40mm 2.0 (Leica or Minolta: better

) : very small, sharp. Kind of difficult to adapt to this very tiny focus ring system. 2.0 kind of short to get the perfect out of focus subject for a good portrait shot to my taste for the moment ... (~400-600$ depending of the condition).
50mm 1.2 Canon LTM : Very interesting lens, very not as sharp as the two Minolta MD wide open, but killer sharp when stop down to 5.6 and more (5.6 portrait ... ? ). The only very unbeatable advantage of this lens is the size and the fact that it take my 55mm filter suite usually on all my other Minolta lenses. Ho I forgot, this lens really don't wants flare ... ouf !
Too expensive option : is to buy the Contax RF adapter and get the old Zeiss/Contax 50mm F1.5. For the moment I'm thinking if I will not sell it once my friend give me back (yes ... I'm sharing too much lens...)
The 50mm 2.0 is very less expensive and there is good Kiev copy also (mostly in the same category of the proposed 50mm by David).
On lens I never touch is the Kiev 53mm F/1.8 that looks interesting
If you cannot wait for the SEL 50 f1.8:
In the AF world with the NEX to AF Minolta Adapter or this great invention (that sometime work better than the automatic one) :
http://www.ebay.ca/itm/Sony-Minolta-MAF ... 3873wt_952
50mm 1.7 Minolta AF : Very good, but focus manually (~115$ on Ebay)
50mm 1.8 DT : can focus on the Sony adapter but very slowly. Good performance for the price. (~150$ on Ebay)
other option : Minolta old 50mm 1.4 (good !) (~250$), or the Sony/Minolta RS 50mm 1.4 (good but more expensive and don't justify the difference).
In the world I know (trying or owning) the winner in the price is the 50mm MD 1.4.
If money is not a problem ... there is VERY good Leica for ~5000$ out there

... and also some in the ~1500$ for smaller aperture.
For signature picture, I recommend the 58mm 1.2 MD and the Canon LTM 50mm 1.2.
Regards,
Frank