I would suggest that there are few basic mistakes to your sentences
The investigation took place in the past;
We look into Holes; we look at pictures
Narrow down what? I suspect you are trying to reduce the number of items so we can more easily make a choice. However when we use narrow down like this it does not sound quite right. What we want is a result but what we are using to describe a result is the action use to obtain said result. So lets analyse this We have a list we want to reduce (narrow down) the number, of chairs on the list so we end up with a short list of chairs.
What are? hmm! Which or what? Which is used for a limited number of choices. What is used for an unlimited number of choices. Well we have reduced the number of choices (narrow down) Therefore I will go with which
However both what and which are used to ask a question, what is the question we are asking?
Possibly the combination of narrow down and what are are being used to mean find?
Best ergonomic; This does not sound correct so let us have a look at what ergonomic means?
"relating to the design of furniture or equipment which makes it comfortable and effective for people who use it": Ref ergonomic
Best comfortable and effective? no this is definitely incorrect lets try
most comfortable and effective; Yes that is OK so we can use
Then we get rid of the clutter we do not need to mention chairs twice in one sentence.
So now we can assemble our sentence
We looked at different types of chairs and shortlisted the most ergonomic. No that's is not what we want to say.We looked at different types of chairs and shortlisted which are the most ergonomic Hmm! still not correct.
Now we get to what I think is the correct, sentence.
*We looked at and shortlisted, different types of chairs to find which are the most ergonomic.