Generally 50mm to 85mm focal length is not too hard to use indoors on FF and does not have much distortion when used for portraits.
It does not mean you must need the fastest lens as its often more important to have enough DOF.
I have taken a few such shots of my own children and the ones I find go for A3 printing have mostly been the ones with enough DOF rather than the absolute least DOF.
So it does not matter if its a f2.8 zoom lens either.
Of course the faster lens has more options to play with.
My advise is to start with a 50/1.8.
Its cheap, its fast for low light and DOF control and its very sharp when stopped down (most 50mms are)
After you have used it and find that you need a tighter crop w/o going too near or need less DOF or more compression, you can consider a 85/1.8.
You can afford both since its within a $1600 budget.
Otherwise, add a nice 100mm or 105mm f2.8 lens if working space allows.
Could even be the Nikkor 105/2.5 Ais, which is not much money 2nd hand.
More importantly, find enough light from natural sources or use a bounced flash, or softbox/umbrella to get enough lighting and good quality light.
My few cents.
20130929-IMGP4472-50 mmPENTAX K-30-1 by
jenkwang, on Flickr
With a 50mm at f3.2 and on aps-c