This is going to be my first DSLR camera. I have used a coolpix p600 before, so now i want great images, instead of great zooms. I have a budget of INR 1.6 - 1.7 lacs for the camera and lens. A new camera costs about 70k INR so i was thinking of getting the SIGMA 70-200mm f/2.8 and a NIKON 35mm f/1.8 with the rest of the money. Although i am interested in wildlife and sports, I don't have the budget for longer lenses and I need the 35mm for family group photos (with the BOKEH). I have no intention of going full frame in the immediate future. Or should I opt for D5500 and go 1.4mm with the money that i will save. Will the extra stop make too much of a difference in BOKEH? Also are there compatible teleconverters for the SIGMA 70-200mm lens?
If the main purpose of the 35mm is group photos, you're probably not going to shoot wide open. f/1.4 vs f/1.8 doesn't inherently change the quality of the bokeh (although the number of blades might at some apertures): what the extra third of a stop (not a full stop) gets you is narrow depth of field, which means that you can have more of the background out of focus. The problem is, when shooting a group you're unlikely to get everyone perfectly positioned on the focus plane, so you either have to stop down to get everyone in focus or you have to take various shots and do focus stacking, which isn't going to be easy because people will move between shots.
There are use cases for which you'd want f/1.4 over f/1.8, but this isn't one.
As for teleconverters for the longer lens, Sigma's teleconverters should be compatible with it, but you may find that Nikon's aren't.
I recently bought a D7200, up from a D3200 and I am very happy with it! It's a great camera, but it might be a bit much to chew for a first DSLR. Have you shot in manual/RAW before? If you haven't, the D5500 is still a very good camera and you're really not going to see that much of a difference between the two. Good glass is much more important than the body in producing quality images. I would personally recommend the D5500 and put the extra money into glass.
The 35mm f/1.8 is an excellent lens. Tack-sharp and at a great price. I own one and would recommend to anybody. I would go as far as to say if you own a Nikon DX and don't own this lens, you're a loon. I wouldn't bother with the f/1.4 unless you specifically need that aperture & have a specific reason for needing it over the f/1.8. (I couldn't think of one)
I own the Nikkor 70-300mm f/4.5-5.6 VR and while it isn't a constant aperture lens, I would actually recommend it over the Sigma. It will give you 100mm more reach also. If the f/2.8 isn't something you have to have, I would go for the Nikkor. It's a solid lens, and the extra reach would be great for wildlife/sports. I bought this lens from Adorama refurbished for $350 USD and it is like new.
If you opt for the D5500, 35mm f/1.8 & 70-300mm f/4.5-5.6 VR, you should be well within your budget & this trio is nothing to shake a stick at.
You could get all three of these for probably less than INR 77843.50. (If I converted that correctly) If I got my conversions right, you've got room left in your budget. Don't forget about things like a camera bag, battery grip if you need it, memory cards, tripods, etc. It can add up.
I would stick with the d7200 because of the buffer and fps of the d7200, as mentioned by Myriad I would stick with the 35 dx for family events and the sigma 70-200 for wildlife and sports.
I use a Sigma 18-35 F1.8 Art DC HSM Lens for my work--photographing biology specimens/experiments/etc...
This lens is also great for family portraits as well.
If you need a longer lens this might not work out but it does have really really excellent bokeh.
why not get a used d7000 or d7100? that's even cheaper. I can recommend the 24-70 f/2.8, I almost exclusively use this lens on my d7000, I think the image quality is far superior to the 35mm f/1.8, the only negative aspect is the price and the weight ;-)