Intern in Consulting for Tech - where?

Good morning everyone,

I'm new at this forum, I hope this applies since I do not have a finance background. Right now, I study computer science & business (with a strong focus on CS) and hope to break in the future from management consulting into a nice tech position - maybe into strategy consulting like this guy (edit: I can not paste the link due to spam protection for new accounts, I am talking about the post from Jun 01).

I'm about to finish year 2/3 of my Bachelor, I've worked for half a year for a big it consulting/implementation company, and next week I will start a 3-month internship at a big4 company. I also have good prospects to do my Bachelor's Thesis with a major car or aerospace company. In addition, I have done 2 years of my undergrad abroad (which is important because I am thinking about relocating to the US, so I want to have good English).

For now, I am thinking about doing a M.Sc. in Management, to get some BA knowledge. Since the uni I am looking for starts a month before I finish my Thesis, I am planning to do a gap year, where I would love to do some internships or a gap year program.
Since my goal is to break into FAANG (or whatever they are called now) into an interesting position long-term, I would love to get some insights or opinions on where I should prioritize my resources for applying for that internship. I know that it all depends on where I get accepted. Should I try to go via Accenture for the connection to tech? Should I just try to get into the most prestigious consulting firm (MBB or T2)?

I'm happy about anything you'd like to share, I am still new in this space and eager to learn! :) 
(edit: I can not remove France from the regions, it just keeps coming back for some reason)