Amogh, 1200D is a reasonably good camera. 150-600 will give you good results if you can handle the ISO & Aperture combination judiciously.
From the available reviews, 1200D appears to be good up to the ISO-800 range as most of birding shots need ISO-800 and above. If you limit the ISO to 800, you have to look at the aperture. From the review of the Sigma lense, it is understood that f/8.0 or more is going to get you a decent sharpness and clarity. However, with limiting conditions like f/8.0 and ISO-800, your shutter speed is going to get below the 1/f limit (multiply the actual focal length by FOVCX factor - 1.6 for Canon crop frames, i.e., at 600mm focal length, the actual focal length is 600x1.6=960mm and the 1/f value is 1/1000 sec) and here the OS is going to come to your rescue. Nevertheless, use a monopod. That's going to help you a lot. The only other factor that is going to limit you is the burst rate, which is low.
Please check the price of the Sigma lens. It may be a little more than your budget. In that case you can have a look at the Tamron lens of same specification.
Once you get the feel, think of migrating to a higher level body, like 7DMarkII or so.
