It would be helpful if you told us what state you are in. Disease and insect pressure varies greatly depending on location and that effects how much spraying you have to do and what you have to spray for. I would first take a look at Alan’s spray schedule to get a general feel for a simple spray schedule.
Spray Schedule- Synthetic Materials
You can modify it to deal with local conditions.
Neem oil and other oils in general are effective for only narrow range of things such as mites and have no effect on fungus that attacks apple tree leaves/fruit or any of the insects that attack the fruit. Generally, you are going to spray it once a year in the Spring or not at all.
Copper is similar in that it is usually sprayed in the Spring only for certain issues.
Immunox is a good choice for Cedar Apple rust. It is prone to developing fungus resistance . To control this you can alternate it with another fungicide or mix it with Captan to reduce the risk of resistance. Also the label on Immunox restricts you in the number of sprays you can do in a year to help prevent resistance from developing. Note Captan is pH sensitive and you will need to adjust your spray water pH to the 5-7 range before adding the Captan since Captan breaks down quickly in high pH water. If you’re interested using Captan we can give you additional information on how to adjust pH if you need it.
Also read all the labels of the chemicals you are spraying carefully. The label restricts what you can legally use the chemical for and the restrictions are based on actual field testing again the fungus or insect you are trying to kill. On the internet there are a lot of claims that Neem oil and copper works against all kinds of problems and that is simply not true.