Equipment for documenting an adventure journey I will be traveling to India in a few weeks and I want to document the journey. Now I'm looking for the right equipment.

There are two constraints: First, the amount of work I want to put into shooting should be just short of dominating the journey. In other words, I want to take my camera everywhere but it should be small enough to not be in the way when I want to enjoy the moment and put it away (I guess everyone has this problem). We will be backpacking and moving around a lot, so I'm not looking for studio equipment or anything too heavy. 

EDIT: I would like to make three kinds of shots: 1) some well-thought-out tripod shots of scenery 2) to take my camera into town on some occasions to get relatively stable footage of everyday life and of my travel partner 3) shots on the go, which can be of the Go Pro cam sort. Instead of making the filming itself less elaborate, I just cut down on the times I pick up my camera. Are these 3 kinds of shots going to give me footage for a travel documentary which isn't just interesting to watch because there's me in it?

At this moment I have a Canon 650D with a 28-105mm L and a 50mm 1.4 lens, plus a good fluid tripod. I would like to improve my footage as much as possible within the space constraint outlined above. 

The second constraint is that I don't want to spend more than 500€ (absolute limit 800€).

I have already considered buying a Rode Videomic shotgun mic to improve audio. What are your thoughts?

If you have been in the same situation before, you can probably help me best. What's your experience?

Best,
Appletree

PS: Help me improve my question. I don't know what information you need to give me a good answer.
PS2: I have already read "What equipment should I get for starting out making professional quality films?" which helped me somewhat but was too unspecific for my situation.
I hate to burst your bubble, but if you are expecting video to be a similar level of intrusiveness to photography, you are almost certainly mistaken.  Video is a much more work intensive process as it requires constant attention to make sure you are getting smooth usable shots instead of the occasional random thought that "I'd like a photo of this."  It is going to take significantly more work and effort to get usable video footage that is stable and well composed.

That said, the amount of effort required varies greatly on what you are hoping to accomplish.  If a "reality cam" style video shot from a GoPro mounted to your pack or helmet and stabilized in post (will still be jumpy and move a lot) is sufficient, then buy a GoPro, a mount, some extra batteries and go to town.  

If you want something that more captures the feel of where you are with documentary like footage to make something that isn't a pure "action shots" montage, you will need considerably more effort to setup tripods, capture proper shots, more planning of the shots, plus the longer time it takes to get the shots.

Audio quality is also something to be mindful of in that situation, as shooting outdoors you are likely to have wind noise and will need to carefully monitor your audio while recording as well and getting decent quality footage might require multiple attempts at the shot.

If you can update your question with a bit more detail as to what you are trying to accomplish, we can probably refine the answer a bit more for your specific situation, but the key thing to know is that it sounds like your expectations of the effort required for a particular type of product may not be grounded in reality at the moment.