I'd just like to say (sentence)

This phrase introduces a comment that you make in a medium-sized group of people, like at a meeting or a party. In a situation like this, if you just make a comment without introducing it like this:

Can I have everyone's attention for a moment? Suzanne, good luck in your new home.

...it sounds too small and unimportant. Starting with "I'd just like to say" makes the announcement feel more complete. As another example is, you can say this in a meeting to the people who work for you:

I'd just like to say that you guys did an absolutely phenomenal job.

on behalf of (a group of people)

Use this phrase when you want to formally make an announcement that expresses the feelings of a group of people. For example, in a written "Thank You" card, you can write:

On behalf of Tina and myself, thank you so much for agreeing to come speak on such short notice. We and the entire audience really appreciated it.

"On behalf of ___" is a fairly formal phrase.

good luck (in/at a place)

You probably already know the phrase "Good luck!", which people say to cheer someone on. You may also know "Good luck with (something)":

Yeah, good luck with that.

But people also say "Good luck in ___" or "Good luck at ___" when a person is leaving to move to a new place:

Good luck in Delaware!

Good luck at your new job.

You choose whether to use "in" or "at" based on what words follow it:

• "in" Boston, France, Australia
• "at" school, your new job