750 is perfect, good enough but not cutting it too close either. Maybe 650 or 700 would cut it, but running heavy OC on 500-550? Not on this planet Earth you won't. Only antivirus I have is the bare minimum program that installs with windows and I've had one virus since I built this PC two and half years ago.
One virus that you know of**** (fixed it for ya)
Anti-Virus is one of those weird things that is basically useless because of how trivial it is to avoid but extremely necessary because of how easy it is to get a virus, even from big websites. One ad in the rotation serving up malware can hit you on any site really.
It does help if you run stuff like NoScript/AdBlock or other similar programs (and DisconnectMe because why not) plus turn off Java/Flash in the browser but nothing is guaranteed. And be logged in as a standard user instead of admin (like most people do, derp.) People seriously over estimate how hard it is to get a virus, it's scarily easy.
As for advice from my end @Hans:
Go with Win7. Win8 was dead on arrival and Win10 is still unstable, and will be for probably another year. If you can't get Win7, go with 10 over 8/8.1 for sure.
I would wait a few months for EVGA/other people to make 1080s, the early buy in is not worth it in my opinion. The card is great but it is not as mind-blowingly big of an advancement as people are making it out to be. Nvidia has had similar leaps in performance in the past. But that isn't to say that I would not put one in a build if I was planning to buy stuff today - I would.
I would caution you... I don't know that buying a whole new rig is going to really give you the performance boost that you're looking for - then again I don't know your current rig, but I assume it is decent from your stream. I doubt going from any i7 to any other i7 is going to have any crazy impact on your gaming, maybe with streaming it will help but even then a capture card would probably be more useful (I am no expert in capture cards though). Overclocking probably won't do much, if anything, for your performance unless your processor is already choking.
The new video card and extra RAM should help (if you're already needing more or faster RAM - make sure your RAM pairs well with your processor).
I would also caution you to be extremely careful or even employ the help of a professional if you do the thermal paste yourself... I think you are self-admittedly not crazy knowledgeable about computers and that part of the process is VERY easy to screw up - and has the potential for extreme ramifications. The rest is more or less plug and play.
Give up on the dream of playing/streaming in 4K for many years unless you are silly rich. You would need a REALLLLLLY expensive rig to play a game in 4K with consistent 60+ FPS, plus a monitor to match... and then streaming it... First - maybe 0.1% of your viewers would be able to watch it in 4K (probably less), and the amount of work your rig would have to do is a nightmare. I am sure this will be standard in the near future, but not for us yet
I think that's all... hope I was helpful/best of luck with the new PC.