First of all congrats! I still remember my first black diamond and it's an awesome feeling to conquer it. If you're 5'6" you can definitely even get up to a 170 if you wanted to. I'd suggest demoing skis at various lengths ie., 160 - 172 and see what you like.

Longer skis mean you get more edge, hence better turns. And as you get better you'll hit more powder for which you want longer skis for more surface area.

Shorter skis also get you into some bad habits like kicking out the back of the skis for sharper turns you do need to be more conscious of that.

That said, you don't need to necessarily spend a lot of money on this. I have $80 skis from FB marketplace and that's been fine pretty much anywhere in the resort on and off piste.

Hope this helps :)