Q: Mobiles have an standard resolution?
A: Nope! Actually you can bet your bum each one will have a different size.
Q: Which is the best way to handle this?
A: Hehe that knowlage is the difference between a junior and a senior dev.
In case of a hud, you will want to ancor the images to the border.
f.i. an image that will sit at the bottom/right should be placed at width/height and bottom|right
In case of 'world' graphics, centre it all on the screen centre.
Generally, code your game in such a style that you have little to no 'magic numbers'.
Don't hardcode image or screen widths.
Don't hardcode relative positions.