Wooden recorders are not inherently better than plastic ones
Wooden recorders require maintenance that plastic recorders do not
Temperature and humidity affect wooden recorders more than plastic ones
Plastic recorders are not indestructible
A "starter" wooden instrument will cost around $$$, depending on the size
Good quality plastic recorders can be purchased for as little as $$.
Hybrid recorders, with a plastic head joint and wooden body are a nice "middle ground" option
Fingering Systems
Recorders come in two fingering styles, Baroque and German. While the German fingering system has a simplified layout for the first octave, above this you will encounter many complex forked fingerings and poor tone and tuning. In addition, the German fingering system is generally only available in student-level soprano and alto instruments.
The Baroque system is the standard for recorders and it is available in all voices. It is strongly recommended to choose a recorder with Baroque fingering.
For your child
Young children usually start on the soprano because it fits their hands well. An older child, however, may be able to start with the alto if their fingers can reach the holes. A child with very small hands may need to begin on the sopranino.
Recorders are not transposing instruments, meaning that a recorder is "in a key". Soprano and tenor instruments are in C. Alto and bass instruments are in F. What this means is that all fingers down on a soprano is the note C and all fingers down on the alto is the note F. From a learning perspective, there is no difference and so size should be the guiding principle in choosing a recorder for a child.
For yourself
Most adults are equally comfortable on both the soprano and alto so you can generally choose the voice you like best. The alto has a lower pitch and a more mellow sound than the soprano. You may also start with a tenor instrument, though many find the reach for the fingers to be uncomfortable. There is nothing wrong with starting on a bass instrument but be aware that you will need to read bass clef and bass instruments are heavier and more expensive.