Buddhists should be vegetarians, shouldn't they?

Not necessarily. The Buddha was not a vegetarian. He did not teach his disciples to be vegetarians and even today, there are many good Buddhists who are not vegetarians.

But if you eat meat you are indirectly responsible for the death of a creature. Isn't that breaking the first precept?

It is true that when you eat meat, you are indirectly and partially responsible for killing a creature but the same is true when you eat vegetables. The farmer has to spray his crop with insecticides and poisons so that the vegetables arrive on your dinner plates without holes in them. And once again, animals have been killed to provide the leather for your belt or handbag, oil for the soap you use and a thousand other products as well. It is impossible to live without, in some way, being indirectly responsible for the death of some other beings, and this is just another example of the First Noble Truth, ordinary existence is suffering and unsatisfactory. When you take the First Precept, you try to avoid being directly responsible for killing beings.

Mahayana Buddhists don't eat meat.

That is not correct. Mahayana Buddhism in China laid great stress on being vegetarian but both the monks and laymen/laywomen of the Mahayana tradition in Japan and Tibet usually eat meat.

But I still think that a Buddhist should be vegetarian.

If there was a person who was a very strict vegetarian but who was selfish, dishonest and mean, and another person who was not a vegetarian but who was thoughtful to others, honest, generous and kind, which of these two would be the better Buddhist?

The person who was honest and kind.

Why?

Because such a person obviously has a good heart.

Exactly. One who eats meat can have a pure heart just as one who does not eat meat can have an impure heart. In the Buddha's teachings, the important thing is the quality of your heart, not the contents of your diet. Many Buddhists take great care never to eat meat but they are not concerned about being selfish, dishonest, cruel or jealous. They change their diet which is easy to do, while neglecting to change their hearts which is a difficult thing to do. So whether you are a vegetarian or not, remember that the purification of the mind is the most important thing in Buddhism.