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Sandy Bridge processors still hold their own these days given how Intel slacked off so badly and only offered around 5% performance improvement with each new generation as they had no competition for a while. Power supply is adequate for most graphics cards. UEFI BIOS so there's no compatibility issues. The only issue is that thanks to cryptocurrency miners the only cards available from both camps are the very high end (Fury X, GTX 1080 series, Titan series) and the very low end (RX 560, GTX 1050).
My advice would be to wait a few months and let the market settle back out, with Ether prices falling and special mining edition cards being released by multiple companies this round of the mining craze should taper out and cards come back in stock. Once that happens, you can go for any you wish. The RX 580 is near 500% faster than your current card, and retailed for around $275 before miners drove the price into the troposphere. Of course upcoming RX Vega will be immune to the mining craze, but will be priced around $400, granted it will carry the performance to justify it.
But a rx 460/560(4gb) is a big upgrade on the 6770, they will pass min. specs on many games.