Streaming and Gaming PC Build, ~$1000, first build

This seems to be your best bet. http://pcpartpicker.com/p/PDGFxr slightly over budget but that's including the monitor. The pc itself is 920.00
This'll allow for 1080p gaming, easily or possibly 1440p gaming. at very playable frame rates (40+)

I was going to suggest a build but I looked at 419Recon's build and it was very similar to what I was going to do for you so I decided not to list it. I will chime in and strongly recommend the GTX 970. It is excellent performance for the price and will allow you to play at a very high level.

I personally would reccomend the gtx 970 for you with your budget of $1000. The performance increase from the gtx 750 ti is very large. I actually always recommend the gtx 750 ti for people who are building on a tight budget, but if gamers have the money for it I always recommend the jump up to a gtx 970 and it sounds like you can afford it.

With the 750 ti you will typically have graphics similar to an xbox one or ps4. If you are happy with that and want to save $200 then go for it. However, if you jump up to the 970 then you will blow the consoles out of the water. Everything will be on ultra at 1080p and will for a while. So if you have the cash I would go for the gtx 970. If you play a lot of games it is really nice to have the eye candy all the time.

Here is a build with a gtx 970 and an AMD CPU. I know you're preference for intel, which I get, but I would consider the AMD FX 8350 if you are concerned about budget it at all. It is amazing for gaming and really performs great. I prefer intel as well, but price for performance I don't think you can't beat this CPU. This comes in at $833.25 without OS.

http://pcpartpicker.com/p/Mmm9FT

Here is the 750 ti with the AMD. It comes in at $603.29 not including OS.

http://pcpartpicker.com/p/gytZrH

Now I can show you the 970 with your choice of CPU, but you already know that pushes your budget up. There is nothing wrong with that if you have the money for it. I probably would, but then again, I spent a lot of money on my build because I can. However, I would not choose intel if that means dropping from the 970 to the 750 ti. That is just my opinion though.

My build is very similar to this video from Tech Syndicate where he recommends and builds a budget gaming desktop. You should watch this video and see if it helps.

https://www.youtube.com/watch?v=uh2_fry7E70&list=UUNovoA9w0KnxyDP5bGrOYzg

In the end, if you have the money for the intel and gtx 970 i would get it all. But I wouldn't invest $1000 in a gaming PC just to end up with a gtx 750 ti. Again, that is a great budget card, but if you spend $1000 on a gaming PC you owe it to yourself to have amazing graphics.

Well to be honest, you wouldn't save too much money (If any). And if you build your system it'll look nicer, be more powerful, and since it is your fist build you'll feel better about it, knowing you're gaming a computer you put together rather than just buying.

Thank you.