Soya milk is a great place to start. It is widely available in supermarkets and is relatively cheap. It works very well in replacing milk in recipes.
If you are following the low-FODMAP diet, it is suggested to go for milk made from soya-protein rather than soya-beans.
Almond milk has a nice flavour, and quite a similar consistency to normal milk. It can be expensive though.
This is not the sort you get in a tin for cooking with. It is thinner and comes in a carton. In the supermarket it is found along with the soya milk. It has a coconut flavour, so you might not want it in your coffee, however it can be useful when cooking.
I find the consistency of rice milk a bit thin, but it could be a good choice if you are not able to eat soya or nuts.
Oat milk has a nice consistency and it has been argued that this is one of the more environmentally friendly options. The barista-style oat milk contains more fat than the standard one and works really well in tea and coffee.