Just a heads up before I answer this: I'm not from the US so not only am I coming from a culture with an entirely different view on guns, I'm also not that knowledgeable about guns or current US gun laws.
-Does the government buy back the ones people already own at their set price
This would be the best way to do it in my opinion. People own those guns legally at the moment so just confiscating them all without compensation is incredibly dicey. You'd effectively be punishing people retroactively.
-Does the government allow the owners to keep what they have but not allow any more sales
This is the second best option, though it would certainly be much easier to do than the first. You would still need the government to buy the stock from gun shops though. It may also be necessary for owners to register their weapons (if that isn't already required) and to report any lost/stolen guns to help combat illegal sales.
-Does the government say you have 60 days to turn them in or else
See my comment on retroactive punishment above. "Hand in your guns or else," implies confiscation to me.
However, doing a buyback scheme and/or sales ban would require a timeframe in which people either have their guns bought by the government or register the ones they already have. If you're going to make certain guns illegal, you need to provide a sort of transition period before you even consider pressing charges against somebody. I couldn't tell you how long that timeframe would need to be but I will say that 60 days seems far too short.