It depends on the monitor.
Macs don't have HDMI 2.0, so you will be limited to 30Hz output if the monitor is bigger than 1920x1080. HDMI will often need a bit of adjustment to settings. Overscan for example, as previously mentioned.
Avoid VGA as it is analog.
DisplayPort is the best option. Is there any reason you didn't mention that as an option? I find monitors waking from sleep is unreliable with any other connection on a Mac.
I didn't mention Display Port because I didn't realize that Thunderbolt2 and Display Port were the same thing. I found a support page from Apple that explained everything to me.
So your answer is a good one, I just didn't fully understand until I read through the Apple Support pages on Display Port & Thunderbolt ports. Actually your answer led me to the solution: mini-Displayport adapter to HDMI cable, which is the advice what Motrek gave. Thanks to both of you!
What resolution? If it's 23" then I would guess the resolution is 1080p.
For a 1080p monitor, I would recommend HDMI. (That is, buy a mini-DisplayPort-to-HDMI cable and use that.) Simple reason being that you could use the same cable to plug your laptop into a TV, which is useful sometimes, e.g., when traveling.
Similar Moonjumper's answer, I now understand my Thunderbolt port is a mini-DisplayPort! So yes, this is probably the best option from what you and everyone is saying.
There is no mention of the need for audio. So yes they are both digital signals. If you want to be technical then yes hdmi carries audio too.
Your right, I didn't mention audio. You are correct - I don't need audio.
Do you also want to output audio to the external display?
HDMI would be my preference and can output both video and audio.
Thanks for the heads up about audio, while I don't need it at the moment it's definitely something I'll probably need in the future when I upgrade. Your suggestion of HDMI was right on the money though, it's definitely the best answer as it simply provides best quality, future proofs with sound, etc...