The ultimate coverage is to patent your solution functionality (utility patent) and aesthetics (design patent) in each and every country around the world. However, practically I chose to patent in a single country usually UK or US to register priority date. Since priority date is the most important element after the patent content itself. If your product is mainly focused on bringing new aesthetics then you can go for a design patent, which usually require minimum documentation and is registered relatively fast. On the other hand, if you have novel functionality digital or physical then you are better off getting a utility patent, however this could take years to be granted. I not a lawyer and this not a legal advice.

It all depends on the quantity. If you are looking for a small quantity, with flexibility in the required design, you can literally search "gym bag OEM" on Alibaba.com If you are looking to penetrate the market with a premium bag, then your best bid is to connect with a manufacturer in Indonesia, where a lot of renowned brands work to produce their sportswear.