I have decided to focus exclusively on concentration as this seems to be a weak point for me. All of my sits have been concentration-focused (this sound redundant but you get it) as opposed to insight focused. I'm doing an hour per day and sometimes two or three 1-hour sessions on weekends or whenever I have more time. I've been following the practice outlined in TMI, i.e. so focusing on the breath at the nostrils and trying to maintain continuous focus while simultaneously not losing peripheral awareness. I was wondering if It would be more beneficial to do a hybrid practice of concentration and insight, or if focusing purely on concentration, at least in the beginning of my meditative "journey, is more beneficial for later insight practice. I should also mention that I have been doing a bit of noting style practice during walking meditation. 

I think a hybrid practice is best. 
https://accesstoinsight.org/lib/authors/thanissaro/onetool.html


My approach is to use samatha techniques to prepare the mind and then to do vipassana. I see samatha more as tranquility/serenity than intense concentration. The biggest sources of mental turbulence are stress and mental fatigue so I find relaxing meditation helps to focus the mind better than intense concentration (which I find causes suppression of thoughts and emotions which is the opposite of what is needed for letting go of attachments and aversions).

I've posted more about my "hybrid" approach on my practice log.
https://www.dharmaoverground.org/discussion/-/message_boards/message/24229477

In my opinion the type of meditation you do, for example noting vs observing the breath, does not necessarily determine whether you are doing samatha or vipassana. You can do samatha or vipassana with either noting or observing the breath. The determining factor, as stated in the quote above, is the "quality of mind"  you are developing. To develop samatha I focus on the object of meditation in a relaxed/relaxing way, to develop insight I notice the activity of the mind - noticing the arising and fading of dukkha (which is equivalent to investigating the 3 characteristics and dependent origination).

So maybe you can do the type of meditation you prefer and start each session calming the mind and then when the mind is calm continue but put more attention on noticing the activity of the mind.

So in practice what would vipassana look like in the context of TMI style meditation. Focus on the breath, then once concentration is stable, try to open the field of awareness so as to observe the 3 c's?

What you wrote sounds reasonable, but I am not familiar with TMI practice. Everyone is different, in my case I don't find intense concentration to be helpful. It seems to quiet the mind but it also makes me irritable which I think is because it results in suppressing thoughts and emotions - which is not helpful. Other people might get different results, so if you find it helpful I don't mean to discourage you.

If this is what happens when you practice concentration try using a more diffuse focus instead of a narrow focus. (I assume by using the word "intense" you meant narrow focus, like a laser beam.)