I received an ice cream maker for my birthday. Never made ice cream before. What should I start off with?

Here's an easy (and wonderful) starter recipe: http://thestir.cafemom.com/food_party/139088/chocolatey_cookies_cream_ice_cream.

I agree with the suggestions for making a premium vanilla ice cream - it will be a revelation, I promise you!

Ditto on Jeni's Ice Cream cookbook; it's simple for first-time ice cream makers and the salted caramel recipe is to die for. I also love this chocolate hazelnut ice cream recipe from Calliope's in New York, and it's not too hard to make:
http://dinersjournal.blogs.nytimes.com/2013/05/22/calliopes-chocolate-hazelnut-ice-cream/

Pierino--can't wait to try that. I thought you couldn't make gelato at home so that's exciting. Thanks everyone!

Now for a Roman Holiday try this http://food52.com/recipes/11377-uncle-fester-on-a-fasta-vespa-espresso-chocolate-gelato-roman-style this is a custard based gelato which is a bit softer and smoother than American ice cream.

I also recommend David Lebovitz's book, The Perfect Scoop. I've given it as a gift alongside an ice cream maker.

I highly recommend Jeni's Ice Cream book. Her technique, adding corn starch, corn syrup and cream cheese, works for all sorts of recipes. It seems to help make the ice cream creamy, as opposed to icy. I also love Ben and Jerry's book, but again, I apply Jeni's technique to their recipes as well. Have fun.

First of all, make sure you have your ice cream bowl in the freezer 24hr before the you are going to use it, it helps a lot. You should start by making an anglaise( creme anglaise), which is like a custard, where you add your vanilla bean/ essence. Thats the base of any flavoured ice creams. Make sure it doesnt curdle, otherwise your ice cream is stuffed already. From the anglaise, you out it in the cold bowl&let it churn, until nice and glossy ice cream :) you can either eat on the spot for soft serve or freeze it down for a little bit harder ice cream.
Good luck and enjoy ice cream making :)

There's no hard and fast rule. You should make what you like best, first. However, it's a good idea to perfect an excellent vanilla ice cream, as it is the jumping off point for so many swirled and otherwise embellished flavors. But if you want to start with chocolate..... just saying

Vanilla Ice Cream. It's one the best foundations for other flavors. I would also David Lebovitz's ice cream book for basics to know about ice cream. For variety I also recommend Jeni Britton Bauer's ice cream book. Brush up on the basics before you start so that you insure success. Some people leap in and then get annoyed that what they tried didn't work.