It is better to use organic fertilizers for a number of reasons, not the least of which is what you are leaving behind in your environment as you garden. However, chemical fertilizers can actually damage plants, causing a speed of growth that weakens the plants to disease and damage in the long-term.
Bonemeal: Promotes strong root growth, use as a base dressing before planting shrubs, fruit, and other perennials.
Plant-based Fertilizers: Such as comfrey, alfalfa, and soy. Use to feed vegetables.
Soybean meal: High-nitrogen source. Use on annual vegetable beds or as a base dressing in poor soil.
Seaweed meal: Helps build up humus levels. Use for annual beds, fruit trees, bushes, lawns.
Rock Phosphate: Use to correct a phosphate deficiency, good non-animal alternative to bonemeal.
Organic garden potash: Use to feed fruit and vegetables.
Gypsum: Supplies calcium without altering PH
If you do need to alter the PH of soil, use ground limestone or dolomitic limestone to make it more alkaline.