My mother, a seasoned farmer, has had no problems planting coconuts right by the house foundation. The challenge actually comes from the tree either leaning on the house or from things falling right on to the house, or people walking below etc. So, leave some distance from the house, at least 2m and if you have space, more. Space them so that they are at least 1m within your fencing. Bananas may be grown in the shade but will need copious water depending on variety.
We also had problems with one coconut tree close enough to the main power line, it became a fire hazard and fire service actually had to be called. I am not trying to scare you. With proper planting, co-seeding and fertilization, you can receive years worth of crops if you have the right climate.
Lemons grow nicely in hot weather, never really get too tall to give shade unless you plan to sit under them. Check with the nursery though, if they can recommend tall varieties. Lemons are very good and worthy trees to grow.
Neem, Indian "strawberries" and mangoes as well as tamarinds can give you plenty of shade, but each will need a good deal of spacing, like 3ft all around themselves or on the sides. In our house and in our farm in South India, we grew all these very successfully, except tamarind, our place being slightly cooler than needed. Almost of all of them will need some soil conditioning.
Teak will need pruning and harvesting, but can be eye catching and give good shade. Make sure they will grow in your area.
Figs are another option, but they can root quite deep and cause hassles.
I wouldn't recommend Eucalyptus unless you have cool climate, live near the coast and/or require wind-breaking. They consume quite a bit of water and are a fire risk in summer.
From what I can tell, Jack Fruit grows tall, in neighboring Kerala where humidity appears to aid it quite a bit. It needs about 1.5 - 2ft or more in spacing, and plenty of patience for the fruit to be produced. They need quite a bit of fertilizing, care and humidity, just so you know.
Before planting, my mother always consulted with the nurseries, and with the local Tamil Nadu Agricultural University. These chats can help you quite a bit, saving time and money. I recommend you do this.