You can consider choosing the colour variation of your logo that is used in connection to your goods and services the most.
By registering one colour variation of your logo, all other colour variations have implicit protection since they are confusingly similar to the original. If someone copies your brand logo but uses a different colour, you are protected. This would be considered trademark infringement.
Sometimes it might be beneficial to register your logo in black-and-white. This is a common practice mainly in the US. This way, you don't have to decide on one colour but rather protect all of them with one submission.
In some countries, such as the UK, it is possible to file a series mark. Series marks may include multiple versions of the same logo in a different colour. They will all be officially protected and included in the trademark certificate.