Scales and Arpeggios
Scales and Arpeggios are essential in developing good sense of hearing as cello learning depends on hearing the right note. There are many misconceptions that cello playing in about training the fingers to press at the right place or feel the right place. However, it is the combination of the eyes and ears at the beginning stage to "learn" the notes. The fingers will have muscle memory to determine the right note after some practices and rely lesser on the eyes. The ear still play an important role in finding and hearing the right note.
Fingering and bowing exercise
These exercise are to train the fingers and the bow arm to work in various ways before reading off notes from the music score. Our body learn best when we train one organ at a time. The first 4 fingers and the bow arm must be well coordinated to produce an accurate sound. There are some important postures to be maintained in cello playing (including all string instruments) for future development. These correct postures are not negtiable as it may hinders progress usually beyond grade 3 standard of the ABRSM syllabus. Thus, it is important to start slow and because of these, your first 10 cello lessons are the most important lessons in your life.
Simple pieces will be learnt to put the fingering and bowing technique in place. However, with diligent practice using the correct method, you will soon be able to play music that you have heard of and music that make you wanted to learn cello. However, certain very nice tone that you hear in CDs and youtube are probably from very good instruments. Therefore, selecting a good instrument (not the most expensive in many cases) with your teacher is essential. Have fun playing!