Can we get a link to the monitor you're looking at?

If you want Freesync support, an R9 Fury or 8GB RX 480 is your best option. The Fury performs better than the 480. The 480 is a newer card and has more VRAM so has it's benefits, and the 8GB 480 would be plenty for 1080p so you could just get a 480. However, there may be a better monitor you could get within budget.

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I will only be 1080p gaming, but wanted something a little more powerful than the 480, but the 1070 is a little out my budget, and obviously doesn't support freesync

I chose the monitor as I tend to go with Samsung for screens, and despite it not being a great gaming monitor it still has a gaming mode, as well as AMD Freesync. It's only £135 so can't moan, can't get a bigger one as I don't have room for it.

I'm swaying towards the R9 Fury as ibe found it for 250, and it outperforms the 1060 6GB, just the age that's putting me off a little.

If you want the Fury, just get it then. It'll be more than adequate for 1080p.

If you want a Fury;
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480's;
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If you're getting a Fury, I'd get one soon while they're fairly cheap, the ones I seen for £250 are already out of stock. An RX 480 would be plenty for you though.

Will the fury be good with the CPU I have? Also, am I better off getting the fury than the GTX1060 6GB

FYI you can't overcloxk the CPU on your current mono and if you don't have an aftermarket cooler I'd advise getting one.

Yes the Fury or 480 will be fine. The age isn't really a big deal as the Fury will still perform perfectly fine at 1080p and even some games at 1440p.

Totally forgot to mention that you're definitely going to want to get rid of that H110 chipset motherboard. You're not going to overclock that 6600k at all with that motherboard, also you can't just expect a 4.5GHz OC. You'll need a Z170 chipset motherboard and a decent cooler for your CPU. What cooler are you currently using on it?

Also, what specific 700W PSU have you got, because of it's bad quality, it won't be safe to use an RX 480 or an R9 Fury on it. If you really want a GTX 1060, get one, it'll be fine for 1080p 60Hz. However, you obviously won't be able to utilise Freesync. I'd personally just get the GTX 1060, but if you want to make use of Freesync, a 480 or Fury are your only options and it's up to you. The Fury will perform better but the 480 is newer, has more VRAM, etc.

And yes, your CPU is fine.

I cant get an exact PSU model until I go home tomorrow, all I remember is that it said 80+ rated or something, not too sure. I was going to buy a new motherboard before I overclocked my CPU, as well as buying a CPU cooler. So the only thing stopping me buying the R9 fury atm is whether my PSU is good enough then, I'll check tomorrow when I get home