Learn Spanish (Latin America): Ante todo, quiero decir gracias.

It acts as a discourse connector meaning "first of all" or "above all." Similar to how you use por un lado to structure an argument, ante todo organizes your speech by establishing your most important or primary point before you say anything else.

Why use ante here instead of antes de?

Antes de is usually used for chronological time (like "before dinner"). Ante often means "in the presence of" or indicates priority. Ante todo is a fixed expression focusing on priority—meaning "above all else in importance"—rather than a strict measurement of time.

Is there a difference between decir gracias and dar las gracias?

In this context, they achieve the exact same thing. Quiero decir gracias (I want to say thank you) is direct and conversational. You could also say quiero dar las gracias (I want to give thanks), which is extremely common but sounds slightly more formal.

Could I start this sentence with just primero?

Yes! You could use primero, primero que todo, or primero que nada. Ante todo is simply a slightly more polished way to structure your introduction, showing that your gratitude takes precedence over whatever else you are about to discuss.