Hi. You need to first decide whether you want to stay on roads or stay off roads or try a bit of both.
First of all, the frame should be a diamond frame- which is the basic frame design you see on most bikes. Some of the new models have odd shapes not making sense and just making the bike heavy.
For city roads you need very little, at least initially. The tires need not be fat and knobbly. You do not need 18 or 21 gears. If you are in Bombay, you can easily get by with 3 or even a single speed. The frame should be the right size for you and saddle height and handle bar height needs to be set right. And you are good to go. A BSA SLR is fine for such riding. With the money you save, you could upgrade the stock saddle and pedals and get a pump and tool kit.
If you want to go off roading, you will want a slightly smaller frame, and fat tires. You might consider front suspension. At your budget, I wouldn't recommend disc brakes or dual suspension. You might need 18 or 21 gears, but at your budget, you won't get trouble free stuff. I have a Hero Thunder MTB and I have ridden the Borivali National Park trails. I love this bike. Hercules Ryder series is also popular. Aluminium alloy frames are lighter and therefore convenient.
If you want to do all kinds of terrain, I would simply recommend a road type bike with fat tires and more ratios. I have seen members here ride the Hercules Thriller, which is also OK. While I have road bikes too, for tackling all terrains on one bike, my hero Thunder Mtb has two sets of wheels, fat and narrow, and that's all. I have done long rides on it. No trouble at all.
All the best.
i hv also bought a hamilton. and its awesome. i'll let you know about the model later on. but its a awesome bike. i ride from wadala to bandra everyday. i would recommend you that bike. it costed me 9k.