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.
Our operating company has twenty years of experience creating and monetizing intellectual property in the US and abroad. I'd be glad to help!
In general, the choice of country for a patent filing has less to do with your citizenship, and more to do with the country in which you are selling your product or service that the patent covers.
For instance, if you have a physical good covered by a patent, and it's primarily sold in the United States and Ireland, but is made elsewhere, you should really only be pursuing patent coverage in the countries in which the good is sold.
By doing this, you can use a patent to prevent someone from selling a product made with the process that you patented in your desired market. You should be less concerned with pursuing patent protection in the country where the product is made, unless you plan to sell your product in the same country.
If you'd like to chat more about this, let me know! I'd be glad to help you create a patent strategy that makes sense for your product.