@Xarick The video card is definitely your bottleneck. The processor should be fine, provided you don't need ultra smooth gameplay, just good enough. Whether to upgrade the GPU now or wait is entirely up to you... If it were me I would upgrade now, GTX 670 simply isn't fast enough (well, I'd have upgraded it years ago to be honest).
GTX 1070 doesn't make a lot of sense to me right now, it's twice as expensive as RX 480 but only 50% faster, and doesn't support FreeSync which will probably be of interest to you if you're upgrading the monitor. Meanwhile, GTX 1080 prices just dropped, it's actually very nearly as good value for money as GTX 1070 right now but will last longer before needing an upgrade.
Two good RX 480 choices on newegg:
Sapphire RX 480 8GB Nitro $195 AR shipped
Asus RX 480 8GB Strix OC $220 AR shipped
Asus is quieter and has longer warranty.
What motherboard do you have? If it's a Z series board, you can quite easily overclock that processor to 4.2GHz with just a quick visit to BIOS: clock multiplier to 42, VCore to 1.200, done. This will improve CPU performance by about 20% compared to stock and reduce CPU bottlenecking in the more CPU intensive games. Of course, you'll want an aftermarket cooler, the stock cooler won't be able to handle 4.2GHz very well. Some cheap and good ones: Arctic i11, 212 EVO, Arctic i32.
Is your current monitor 60Hz or 144Hz? If it's 60Hz, I would probably buy RX 480 and then upgrade the monitor to 144Hz FreeSync next. Samsung's curved 144Hz VA monitor C24FG70 would be nice and I've heard good things about it. It's not the cheapest one though, and it's still just 1080p. If you want 1440p, you may have to upgrade the graphics card again when upgrading the monitor.
Do you have an SSD for the OS, programs and games? If not, you're missing out
As for the RAM, I doubt you will need more. You can easily keep track of RAM usage in Task Manager. If you're not experiencing slowdowns that are clearly RAM use related (not mere hitches but proper slomo stuff), then you don't need more RAM.