I guess you can make argument for all 3 options here:

You are getting 4-1 to call preflop and have better odds than that to flop an A or Q flops and then fold if it doesn't (If you have any intention of trying to bluff post flop you should definitely push preflop). This saves you risking chips with A high when he is likely to call your shove with any pair.

The min raise may be taken as suspicious and therefore look like JJ+ in which case you should fold. You have enough chips that you don't need to get involved.

Or my personal favourite PUUUUUUUUUUUUUUUUUUUUUUUUUUUSH.