You don't have to be from a computer science background to do this, but you need to be a good Business Analyst to do this. You need to clearly define all your processes, it seems like you are trying to do this for a small operation, at a high level here are the components you would need
1 - A basic WMS - where you can receive product, locate product with a decent amount of visibility then ship product
2 - With the one above you will have a decent inventory control system, that means you will know where your inventory is and how much you have on hand or within the 4 walls of the warehouse
3 - Then you need to have an Order collection process, where this process will read all your other systems that is receiving orders and download them into your WMS
4 - Then fill the orders from your WMS
It is relatively simple at a high level, you need to establish processes in place after analyzing your business and come up with systems to process those orders
Also have the right tools to process those orders, like a wearable computers to do picking etc. You don't need computer science background, you need to establish simple processes to execute everything, in fact I would say computer science background is bad to have because people with such back ground tend to think in a complicated manner and would come up with much complicated processes but what you need are dumbed down processes that anybody that you can hire from the street at $12 to $15 per hour, that can execute such processes.