What's the first thing I should make with my mandoline?

Spend some time running test samples with the mandolin to try the different blades and thickness with different vegetables. Seems easy on paper but it can really make a difference when you actually want to use it for a real recipe. I bought a PL8 mandolin a few months ago (research, youtube videos, etc) that looked really easy to operate but when I tried it at home, it was a lot harder than I had anticipated. Returned it and have my eyes on a Benriner now instead.

What do you like to eat?

I'd watch this.
https://www.youtube.com/watch?v=iCMGPRiDXQg

Put your copy of "The Rat Movie" aka "Ratatouille" on, and make Thomas Keller's version of the title dish. What?! You don't have the movie? Now that you have a mandoline, you need it more than ever!!

And yes. Get those gloves.

sauerkraut or kimchi

Beet (and other root vegetable) chips -- simmered in a sugar syrup and then baked. The original recipe calls for a curried sour cream dip; I use the spiced yogurt from the Mujaddara w/Spiced Yogurt recipe instead -- lighter, and since I was living in Tajikistan when I first made this, I could make the yogurt.
The recipe is from Epicurious: http://www.epicurious.com/recipes/food/views/beet-chips-with-curried-sour-cream-109510

Pear chips! https://food52.com/recipes/14417-kale-salad-with-fried-pear-chips-and-toasted-walnuts

1) Get Kevlar gloves. Do it now. Amazon.
2) Gratin potatoes
3) Pear pie the dense stack crumb topping way.

Beet chips! The prettiest, and so delicious.

A quick look to make sure you a first aid kit on hand. Those things require a blood sacrifice. Yeah..you say you'll always use the guard except when you just 'need that one thing quick'.

Francis Mallmanns Domino potatoes https://food52.com/recipes/20592-francis-mallmann-s-potato-dominoes

Potato chips! Nothing quite so wonderful as home-made, fresh potato chips. :)

When I first got a mandoline many moons ago, I went on a Pommes Anna bender. It's sort of the perfect food: https://cooking.nytimes.com/recipes/1018518-pommes-anna
Also, cucumber salad. And zucchini "carpaccio".

I do not have a mandolin but I am planning to make these okonomiyaki tonight. They look like one of the most popular recipes on the site: https://food52.com/recipes/12352-okonomiyaki

I use mine for salads and if you have any interest in kimchi--slicing turnips for turnip kimchi is fantastic!

A salad including raw shaved root vegetables that are often cooked (out of necessiry or custom). Kohlrabi, celery root, parsnip. And others that aren't root veg, but taste good in thin slices.

Penelope Casas' "poor man's potatoes".

Potato chips!!!!!
Here's a link:https://food52.com/recipes/27915-rosemary-potato-chips

A root vegetable tian? Can't imagine making one without a mandoline!

Or I've had my eye on this salad for ages but have never made it -- http://www.101cookbooks.com/archives/moroccan-carrot-and-chickpea-salad-recipe.html

How about vegan lox, made with carrots: https://food52.com/blog/16630-what-looks-like-lox-tastes-like-lox-but-is-made-of-carrots

Ok, maybe not ideal with a long carrot, but you could make smaller strips.