The ancient Israelites, naturally, had a lot of sheep. Comparisons of the house of Israel to sheep, with the Lord as shepherd, are scattered throughout the Old Testament. David started life as a shepherd, and compared the Israelites to sheep. The Psalms are filled with the same comparisons, most famously Psalm 23. Isaiah, Ezekiel, Jeremiah, and other major OT prophets use it as well. In short, the house of Israel as a flock of sheep, and the Lord as their shepherd, is a major metaphor in the Old Testament.
Jesus, of course, was very familiar with the Torah and the prophets, and quoted scripture liberally. He called his disciples his sheep, told parables of lost sheep, and called himself the Good Shepherd. He commanded Peter to feed his sheep.
Also, Jesus himself was referred to as the Lamb. During Passover, the Israelites were commanded to sacrifice a lamb, which must be a male of the first year, without any blemish or injury. Christians see Passover as a foreshadowing of the sacrifice of Christ himself, which is why he is called the Paschal Lamb.
So, why sheep? Several reasons. In Israelite times, a shepherd would really lead his flock, and they knew his voice. Each shepherd would have a distinctive call, and when he gave it, the sheep would follow him wherever he went, so that he could lead them to a fresh pasture. It was not, however, a prestigious job; shepherds were near the bottom of the social ladder.
Now, sheep are not any too bright–in the words of my bishop’s wife, whose family raises lambs, they “are born trying to die.” They need someone to lead them around and show them what to do, and they’re very good at getting into trouble, but not at getting out of it without help. They are greedy, too. And they are heavy and clumsy to carry (that romantic image of Jesus carrying a sheep across his shoulders is an actual way to carry a sheep, but it isn’t easy!). However, sheep do have personalities; they’re individuals, and a good shepherd knows each one well.
It strikes me as an excellent description of people. None of us are any too bright, either.