It depends on what you're talking about. Java2D? JOGL? libGDX? Something else?
Just the standard drawImage method.
I wouldn't say there is 1 best resolution, but rather the native resolution of the screen is the best.
But different computers & monitors have different resolutions. My 24" monitor has 1920x1080 while my Linux laptop is 1366x768 while my old netbook is 1024x600. If the game adapts to different res then obviously the game difficulty changes. I was kind of hoping that someone could just say "you just need res NxN and it will work perfectly everywhere". At least that's what I was hoping.
That's strange, I've never seen that before and a Google search didn't yield any results. Maybe a code sample?
The code is quite simple stuff
public final Font Charfont = new Font("Impact", Font.BOLD, 30);
og.setFont( Charfont );
og.drawRect( x,y+10,120,40 );
og.drawString("Set up", x+26, y + 40 );
On the PC the text appears perfectly centred in the rectangle, on Linux it's off to the side. Thinking about it, it may be the fonts that are wrong - but I would of thought if you specify a particular font then you'd get that font.