If you want to make the right choice first of all you need to analyze the needs and the capabilities of your business. And there are some more factors you need to consider but for two above mentioned: geographical location of customers and the type of business.
These factors are the location of your business, your processing volume, prior processing history, some specific requirements of your business, for instance, the ability to accept multi-currency or micro transaction. These are just some points and the list can be extended further.
Also, I can share with you one informational resource called #Paylosophy where you can find the articles describing different issues of payment processing industry or if you do not manage to find the answer to the question you are interested in in one of the articles, you can ask a question there.
You are just starting so I can assume that the processing volume is not expected to be very high, so a service like PayPal or its alternative is probably going to be the best option. You have already been provided with a lot of PayPal alternatives but you also can have a look at Skrill, Braintree and Payoneer.