Some info about you will help... You're new to iPod shuffle. Are you also new to using iTunes? Do you know how to load songs on your shuffle using the manual method (the way it is now set up)? Do you know how to create playlists in iTunes? Is your computer that runs iTunes a Mac or Windows PC?
Here's a method called Autofill, that is convenient for iPod shuffles. I usually use this method with my shuffle. It's not automatic syncing, but it's easier to explain without knowing answers to the above questions.
Connect iPod to the computer running iTunes. It appears as a small button on horizontal bar that goes across iTunes window (where you found the Eject button). Click that iPod button to select your iPod, and iTunes window becomes your iPod's Settings screen. There is a sidebar (column) along left side of iTunes window, with a small picture of iPod and your iPod's name at the top. In that sidebar, look underOn My Device and click on Music there.
To the right, iTunes window now shows the list of songs that are currently on your iPod. Look near bottom right corner of window, to find the Autofill button. Click the Settings button next to it. In small window that comes up, put checkmarks in the two checkboxes for Replace all items when Autofilling AND Choose items randomly (if they are not already checked), and then OK. Over to the left of the Autofill and Settings buttons (along the bottom), it says Autofill From. Make sure Music is selected there (should be already) from the dropdown list.
Now, click Autofill button to load your iPod with randomly selected songs (as many as will fit) from your Music library (which you said has about 700 songs currently). This takes a bit of time; you'll see progress on iTunes window. The capacity bar at bottom of iTunes window shows how much of iPod's storage space is used. Autofill will fill it up completely with songs, since your total iTunes music library is (probably) more than your iPod can hold. When you want to fill your iPod with a new randomly selected set of songs, just use Autofill again.
With this method, your iPod is still set for manual syncing (because you "manually" click Autofill button to start the process). So the iPod's light will keep blinking orange (after Autofill is done) until you Eject the iPod (like you did earlier). Just remember NOT to disconnect iPod if you see the light blinking orange, until after you Eject it and the light become solid. To listen to your iPod, just move its on/off switch all the way to the "shuffle songs" position.