Can I avoid additional costs by registering both word and image trademarks in one application?

No, it is not possible to file one application with two trademarks. You need to file the wordmark in one application and the figurative mark (logo) in the second application.

Trama can offer you a reduced service fee for the second application if all the information is the same and the two trademarks differ only in type.

You can theoretically register a mark that combines the logo and the brand name. However, remember that you wouldn't be registering a word and an image trademark in one application; you would be registering a new figurative mark containing text. This would have implications on your level of legal protection - for example, you wouldn't be able to use the ® symbol with your logo and brand name separately, only with that combined mark.

That being said, it is indeed a more cost-effective option, and many businesses choose it. It is also a good option for brands whose name is too descriptive/generic and who wouldn't otherwise have a chance of registering their name as a wordmark. So it is a viable option; just be sure the combined mark is the one you want to represent your business.