Probably bottle stoppers. Pens aren't hard either, but slightly more difficult to make the proper diameter.

 

A great big ol' pile of sawdust!

 

Grab a small tree branch, mount it between centers, true it up with a spindle roughing gouge then practice some cuts—coves, beads— with a spindle gouge.

Look online for Youtube videos which show this process.

Keep going until the tree branch is completely transformed into shavings then do it all over again with another branch.
Once you kinda get the feel for how the tools cut, begin to make coves and beads as close to identical as you can. Try to get control of the sizes. Then do it again. And then again.

Meanwhile, while you're watching teevee or drinking morning coffee, make sketches of a combination of beads and coves and such on a piece of paper. Play with the shapes until you get something that pleases you, then grab another tree branch and try to make exactly that shape.

What you're making is fancy sticks, basically, but that's teaching your hands what to do so that what you end up with is something close to the image in your mind. The big advantage to this approach is that there's no way to mess anything up. There's no such thing as a bad stick, there are only sticks which don't come out the way you pictured them.

There is no other way to learn this. You cannot think your way to understanding this link between hand movement and the shape of the finished product in your mind—it's muscle memory and doing it is the only way to get there.
And all your future turning satisfactions will be grounded in how well you teach your body how to respond to the process and the material. All of it.

Use green tree branches, because green wood is so much easier to turn than dry wood and much less dusty.

Then make maybe a light pull, or a kitchen cabinet knob, or just a decorative thingy which ends up in a plant pot for a little houseplant to grow up.
Maybe a handle for a lathe tool.
Maybe a handle for a coffee scoop using an old sawed-off teaspoon or tablespoon you find in a junk shop. Or a basting brush for the kitchen using bristles you can buy for that purpose.

Then start thinking about what you'd like to make, and why. For sale? For gifts? For your own household? All of the above?
Pens are simple, as are bottlestoppers. Cabinet knobs. Handles for all kinds of things.

A simple box with a lid that fits it is a challenge in the beginning, but enormously educational.

Move toward bowls (facework) only after you've gained some confidence with using tools in spindle orientation. You'll get catches in the early going without a doubt. Everyone does. And while catches in smallish spindle work can be startling, they're rarely dangerous. Catches in facework can be more serious.

Be careful and wear a face mask.

I originally started this post with "here's my two cents" ... but I just deleted that because I see now I kinda went on a bit of a rant.

 

Kindling. seriously, the first things you make on any new tool, and a large especially, are going to be scrap. Best to do like 9kfeet said, and just mount up a piece of whatever and practice the basics. I'd mill a piece of 2x4 square and use that over a random stick though.

Once you've got the basics down, make your first project something you need. First thing I needed was tool handles, so I made those

 

+1 what epic said! Ya might have big ideas, but start small & work, not the other way around. Be sure & keep your chisels sharp, my friend! I'm still green myself, & have had more fun learning the lathe than any other tool I own! I've done some things on the lathe I never thought I could, ya just have to start playing with your tools, & learn what they do & how they do it. You'll be amazed at what you can turn out! Have fun, & be safe! And by the way, to ask what the easiest project to make on the lathe is, what can you dream up?������

 

Be sure & keep your chisels sharp, my friend!

This. So much this. We need more focus on this. The first thing you need to do when you get a lathe is sharpen your tools. Turning is secondary, you wont do anything without sharp tools

 

Kindling. seriously, the first things you make on any new tool, and a large especially, are going to be scrap. Best to do like 9kfeet said, and just mount up a piece of whatever and practice the basics.

I burned my first several pieces. I got the wood from the firewood pile so it was sorta like recycling. I used to bag up the shavings and burn them, but after I started turning bowls that idea was quickly abandoned.