I understand that meat will give me essential amino acids, but I can get them from good vegetables
No you can't! Meat and animal produce (milk, cheese, eggs. etc) are the only source of first class protein. Vegetables are high in some of the essential amino acids your body needs and low in others. Whilst grains, legumes and fruits can provide the others.
You need to ensure your daily diet contains the following:
Whole grains - Bread, pasta, rice, tortillas, cereals.
Legumes - Peas, beans, lentils, soya products such as meat substitutes and tofu.
Fruit - Vary as much as possible.
Vegetables - As with fruit, variety is the spice of life.
You should build your meals around the whole grains, eat plenty of fruit and veg and try to get some form of dairy product included with each meal even if it's only a yoghurt for dessert or a glass of milk with your meal.