R10k won't get you very far if you plan on buying from a decent audio shop ....
Remember with sound, people can say what they want, what sounds good to me, might not sound good to you.
So firstly remember that, you have to listen to the sound before you buy. There are many brands out there, difficult to choose. One
of the things you can consider is that on your budget it might be better to start building the system piece by piece instead of one shot. That way you can save up and over time get a better quality set than settling for lower end stuff up front.
Look at how big your room is and how big sound you need or want. I have a Marantz receiver that has Audisey sound setup included. Once setup with some tweaks it works great. With auto adjust on sound no more loud tv ads for me. So I am happy with it, but you might not be.
Start with the receiver do you homework see what is out there and at what price. I know the NAD receivers are quite good and also comes with Audisey. Look at how you would want your sound setup 5.1 / 7.1 what will your needs be. Then look at how much watts per channel you would want, sounds silly but also don't be fooled by big numbers on some brands. Look at how many devices you intend to have setup on the receiver and make sure it has enough inputs.
Once you have settled on the receiver you like. Then start looking at speakers and what's left of your budget. That is why I would suggest building the system piece by piece and over time. Best would be look around at the different audio stores and speak to the guys. Remember just because you are in a audio specialist store, don't think that the sales people won't sell you bs just to make a sale either. Remember some speaker "packages" the speakers are good but sometimes the sub not so good so when going for speakers maybe get the sub seperately. I currently only have a 5.0 set speakers, but now I can shop until I find a decent sub that I am happy with and won't be stuck with something I don't like.
For your budget you could even go to DionWired as a start and look at the different options they provide, as they stock the normal stuff you can get at game, and they stock some higher end stuff like Onkyo/Marantz. Just to get an idea of those brands and what they can offer.