Whether you should trademark your logo, brand name, and slogan simultaneously depends on the level of protection you are looking for and how you use the mark.
If, for example, you use the logo, brand name, and slogan together, you can include them in one application that will be filed as a figurative trademark. However, you should be careful here, as the individual elements of the mark will only have implicit protection. If, for example, your logo merely consists of a generic shape or isn't very unique, someone can use it without infringing on this trademark that combines all the elements. Similarly, if your brand name is descriptive or lacks uniqueness, it can get copied.
If you want to protect all the individual elements, you can file three separate applications. Here we recommend making sure the elements are registrable before filing. You can do so by using our free lawyer's check.
As for slogans, they are often difficult to register on their own. Slogans or taglines usually do not fulfil trademark requirements. They often fail to distinguish the origin of given goods and services from other goods/services. For this reason, if you wish to register your slogan, you can do so by combining it with a brand logo/name. However, the slogan itself won't have the full scope of protection. It will be protected only in combination with a logo or a brand name.