What resolution to make my website for?

I'm having an urgent question;

In 2008 I created my website (budopower.com)... and at the time a resolution of 1024x768 seemed to be the best choice, on behalf of several forums.
So back than I made my website around that resolution, staying on the safe side by keeping it 1000 pixels in width.
I used 1024x768 as well on my personal laptop.
In 2010 I switched to 1600x900 (for personal use), but didn't touch my website resolution and left it at the previous mentioned 1000 pixels in width.
The site looks pretty descent, viewing at 1600x900.

- Now (4 years later) I recently switched to 1920x1080 on my personal laptop... and now I start to notice I have quite a bit of black (empty) space on both left-/right sides.
The site just looks a bit narrow when viewing at higher resolutions.
Also, the letter font seems to be a bit harder to read, or is that just me?
So I'm starting to think about re-doing my whole website, although I;m not quite sure what resolution would be the best choice to do that in?

* I don't even know IF it's a wise thing to do, re-doing the site in an other resolution?
I mean, what resolution is the most common these days?
(I want to be safe, not being forced to redo it AGAIN in 2015)
Of course I could just go for a bigger letter font and leave the width as it is - at 1000 pixels -, but still it does look a bit narrow for people (like me) who use somewhat higher resolutions...


--> So what do you recommend me?
(bigger letter font, change my resolution... if so, what size)

Thanks