Which PhD program should I choose, a top three program without any guarantee of funding or a top 50 with full funding?
Accept the funded offer.

There is (I think) a general consensus on this site that the quality of your own research as a PhD student matters much more in the long run than the reputation of the university you're at. A PhD is stressful enough without you having to worry about money as well (food, rent, bills, tuition- the list goes on).

The only advantage I can see in attending a top "name brand" university (for example, Oxford or Cambridge) is if you leave academia for an industry job, where the name of the university is likely more familiar to a prospective employer than the name of your supervisor.