How much I actually need depends very much on one thing: Will I get free medical care when I need it, or will it consume hundreds of thousands or millions of my accumulated dollars?
If I assume that the free medical care will be limited or absent, then I need several million to be able to pay for my rejuvenation treatment at age 90! (Or cancer treatment, custom stem cell line replacement organs, nano-tech joint & bone repair, etc.)
If that worry goes away, then my needs get much more modest. For example:
1) Housing - A small apartment with some community facilities (IE. a pool) would be fine.
2) Food - Nothing fancy, just some fresh produce and clean meat & fish will do. (No caviar required, no gourmet wines, and no Ruth's Criss either.) Just give me a weekly pass through a working-class buffet line like Soup Express, for my "fine dining" entertainment.
3) 100 digital TV channels or so, for passive entertainment.
4) Internet access with enough bandwidth to enjoy video streams.
5) A dog or two as companions.
Depending on where I live, I think this could all cost as little as $30K/year.
The concept of finite wealth actually strikes me as a good idea. In much of the US we see gun ownership as a fundamental right, but we would not permit private ownership of nuclear weapons. Money works the same way: Having enough to make a good life for you and your family is a terrific thing. Having a vast fortune permits you to do some very bad things to the rest of us. Most people have no idea of how much power goes along with having $1 billion in the bank.
Dynasty: Bad! I've already posted in this thread about the destructive effects of leaving a fortune to your heirs. Destructive both to them and to everybody else. No surer way of creating a bunch of worthless lazy arrogant a-holes. Easy to fix: Get rid of the Estate Tax and replace it with progressive taxation of all inheritances above a modest limit as regular income. A tax-free limit of $1 million would work okay. Plenty for an education, starting a business (or buying into a parent's business), et cetera.
