The cello is a popular string instrument and comes in various sizes for different ages of beginners. Young children may start on a 1/4 size instrument, progressing through to a full size (4/4)cello at around 12 years depending on their growth rate. Because children outgrow instruments quickly, it is often better to buy a secondhand instrument but if you do this be careful to have someone with you to check the instrument is in good condition and is fully playable.
Most parts of a cello do not wear out, with the exception of the bridge, strings and sometimes the bit at the top of the instrument where the strings cross the neck. Bridges are easy and cheap to replace, student strings are also inexpensive. From time to time a new bow may be needed or, more commonly, it may need the horse hair replacing.
In terms of a case, if a child is carrying a cello on public transport or if the instrument is very valuable, a hard case is best to prevent damage. If the instrument is only moved in and out of a car, a soft case is possible but care must be taken to avoid knocking the cello at all, especially around the bridge area.
Cello music is written in bass and tenor clef. There are a lot of cello tutor books which start with teaching the instrument using popular tunes and nursery rhymes for young children.