No method is the best for what you want to accomplish. There are many different methods that you could choose, all of which will provide you with information that you can use to improve your user experience. None of the methods will provide you with perfect information.
You could conduct 1:1 interviews with your current users to learn about how they use your service. You can craft your interview script to gather data. The downside of this method i that you are asking users to reflect on their experiences, so they might not remember everything, or their memory might be colored by parts of the experience that you don't understand because you're only hearing them talk about their experience instead of observing them when they use your service.
You could conduct a usability study of your service. You will learn about what works and what doesn't in the experience of ordering lunch through your service. The benefit is that you can control the experience and can focus your study on specific aspects of your service. You won't necessarily learn about other aspects of the experience that impact their satisfaction, such as the delivery or the quality of the food that they receive.
You could conduct a survey, which will give you access to a lot of people (including people who haven't yet used your service, or people who used it once and decided against it). You can learn a lot in a well-crafted survey, and you can gather it quickly and easily. As you observed, you don't necessarily get a lot of context about the data.
If you have never conducted any kind of research, I would choose whatever method you feel the most strongly about and do it. You will learn something about your service and your users, and you will learn more about conducting research. Both of these will help you create a better service. Choose a method, read up on it so that you can do it well and collect unbiased data, and do it. Learn from your research and then do some more. Don't get stuck on conducting the best research. Focus on learning more about your users in a way that will impact your service.