Classical guitar is a fascinating instrument to learn. The process of graduating from struggling to get your right hand fingers working to playing bass, melody and accompaniment together will keep you enjoying your guitar practice for a long time. Not that it takes that long before you are playing easy classical songs.
One of the things that the beginner classical guitar player notices is the noise his fingers make when his hand moves up and down the neck of the guitar. This has sometimes put potential students off learning to play. The sound of the fingers rubbing the steel-wound bass strings is sometimes louder than the music he is playing. You will find from experimenting that some strings have this problem more than others, but you will also develop the knack of lifting the tips of your fingers slightly when changing position without losing any accuracy in your playing.
In centuries past, what we call classical now was the only guitar style that existed. Whether it was accompanying songs or playing instrumentals, the music that was the product of strumming and plucking the guitar strings inspired many composers to write easy songs and pieces that could be played on the nylon string guitar.
You don't need to confine yourself to classical songs and pieces in your repertoire, there are lots of arrangements of modern tunes for classical guitar. Apart from the classical guitar versions of songs by The Beatles which have been around for many years, classical guitarists have posted on YouTube videos of their arrangements of songs like Stairway To Heaven. The videos often provide a link to the tab for the tune so you don't have to learn it by ear.
One of the most popular easy classical guitar songs is Blackbird by The Beatles. Everybody loves to play it and audiences love to listen to it. But there are easy songs and tunes from all ages that you can play after a few months of learning guitar. You can even find anthologies of easy classical guitar pieces such as 50 Easy Classical Guitar Solos by Jerry Willard. This book contains pieces from all periods of musical history written in standard musical notation and in tab form.
There are also collections of pieces by Johann Sebastian Bach like Sarabande No. 1 and Musette in D Major that are surprisingly easy for beginners to play. Also there are well known anonymous pieces like Packington's Pound, Nonesuch, Kemp's Jig.
The best thing about learning easy classical guitar songs is that many are beginner-friendly pieces that will yield great satisfaction without being difficult to play.