John Lee, with most things in life, knowledge is power. The more your learn and know about various aspects of gardening, the more able you will be to to make informed choices about how to care for your garden and help your plants to thrive.
Compost or well aged manures are great additions to any garden setting. They will assist in improving soil structure, help to retain moisture and nourish and encourage a healthy soil biology. They do add to soil fertility as they break down and release nutrients but slowly over time and not to a significant degree. And for many types of plants, that may be all that is necessary. I have always mulched my gardens with compost on an annual or sometimes, semiannual, basis and for the vast majority of trees, shrubs and perennials, that yearly or twice yearly addition of organic matter helps to provide all the nutrients they require. I have rarely, like almost never, had to resort to a commercial fertilizer and only then when a specific plant was showing a specific deficiency.
Annual plants, like most vegetables or those that are cropped/harvested, may require a different approach. First, they have different nutrient requirements due to their short lifespan and need for high productivity. They are often considered to be 'heavy feeders' or demand and pull a lot of nutrients from the soil in a short period of time. Compost or manures may be inadequate in terms of providing fast access to the nutrients they require as well as in the amount of nutrients they contribute.
This is where fertilizers come in handy. They are a known quantity so you can apply precisely what is needed. And commercial fertilizers are available in both synthetic/manufactured formulations as well as those that are 100% organically derived, so you can use whatever approach you prefer. Dry organic fertilizers are not water soluble and like compost or manures, take time to release nutrients so those need some lead time to be fully effective. You have to be able to anticipate the plant needs in some respects and that becomes much easier with more gardening experience. And as Richard noted above, there are blended organics (Espoma products are an excellent example) that can address a range of nutrient requirements.
Homemade organic fertilizers become a lot muddier in terms of knowing what is being provided. In most cases you are just guessing and in any event, the nutrient output may be minimal as well as delayed. One of the ways around this is to make your own blended organic fert using known quantities, like blood or bone meal, alfalfa or other seed or grain meals and rock dusts. But it does take a bit of math to figure out what percentages of what nutrients are being provided so most just shortcut this step by purchasing and using a prepared mix.
Compost or manure teas or those brewed from discarded plant parts, as well as worm composting leachates, can also supply some nutrients but again, they are unquantifiable so to a large degree an unknown factor in nutrient supplementation. Their big advantage is that the nutes they contain - whatever they are - are immediately availble for the plant needs..
One type of product - compost, manures, commercial synthetic or commercial organic ferts or even the teas - is not necessarily better or worse than another. They all have pros and cons associated with them. Becoming familiar with them all and understanding their attributes and their drawbacks as well as knowing what the requirements are of the plants you are growing will help you to make the most informed choices. It is definitely an experiential process but the more you garden and learn/research, the shorter that time frame will be.
Q