It probably will show up. The impact to employment depends on the companies rules and would be more likely to be disqualified if you were asked if you had an warrants and said no (lying)
Gun permits would not likely to be hindered. Normally the only things that would stop you from being able to purchase a gun is a felony conviction or a history of mental illness. There may be cases where a person that has been convicted of domestic violence would also cause you to not be able to purchase a gun. You would need to check the laws in your state.