Should I live in someone else's property for free or should I house hack?

I would take the free rent in exchange for management, for the simple reason that it's zero risk. You don't say whether you have previous experience doing property management. (If you do, you can disregard this.) Suppose you buy the house, rent out the rooms, and then discover that you hate doing that sort of management? Or worse, that you can't actually rent all the rooms consistently enough to pay the mortgage? Then you have a lot of your money locked up in the house, whereas if you're doing the management for someone else, you can just give them notice and move out.

Home ownership is an important piece of many retirement plans. The idea of paying rent or having to move any time a landlord doesn't want to renew your lease at 50+ years old doesn't sound pleasant to me, but many people are life-long renters, you just need to craft a plan that suits you.

Even if you do want to own a home eventually, it doesn't have to be now. Being a property manager in exchange for rent will give you good experience without much risk/financial responsibility. That sounds like a great opportunity to get your feet wet and find out if being a landlord is right for you. That's assuming that this property management gig is just part-time in addition to your normal work and you aren't foregoing significant income (enough to cover rent) by taking the opportunity.

I wouldn't try to do both (at least not right away). I got started being a landlord by buying a 2nd property to live in and renting out my first property, that route has several advantages: You can get a lower interest rate if it's your primary residence, you can do less than 20% down if desired. It also gave me a good while to try being a landlord without sacrificing the capital gain tax exclusion if I decided it wasn't for me.

I'd take the free-rent property manager gig unless it was going to take up too much time for it to be worth it from an hourly pay perspective. Use that experience to decide if longer term you think you want to be a landlord or if you even want to own property.