I am planning on buying a Canon 77D which will be used mainly for vlogging. I wonder which lense I should start out with? The one that is included in the package is a 18-135mm IS. Would that be a good start?
I would advise against buying the included kit lenses (18-55mm, 18-135mm) altogether. Ideally you want to find a lens in your price range with the LOWEST possible f-stop value. The kit lenses range from f/3.5 to f/5.6. You will want to aim for what is considered a 'fast' lens -- ideally with an f-stop of f/2.8 or lower. You will give up the ability to zoom, but the cheapest and best lens you can get for any DSLR is a 35 or 50 mm f/1.8. These will run you under $200 and the image quality will be leaps and bounds above what the kit lens can achieve.
If you want to be smart about it and don't mind paying a bit more today so you can save money in the long run, don't get the kit lens is the rule for DSLRs. For vlogging, you will want a lens around 24mm (35mm is still doable when recording yourself in selfie mode but it's still too much zoom for this job). As beepIT says, you will want a fast lens. In the particular case of the 77D you can actually get a fast lens for vlogging for the same price as the kit 18-55mm lens. I'm talking about the Canon EF-S 24mm f/2.8 STM Lens. This one doesn't come with Image Stabilization, which is okay because the 77D has its own stabilization for video.