If working in the US right after school is more important to you than the actual job itself, then you should go to Georgetown. INSEAD is a great school, but it's simply going to be harder to do the job hunting thing for US-based jobs because it's on a different continent. Plus, it's a one-year program so it doesn't match well with the traditional recruiting cycles for US-based banks.
If you want to do banking as a career switcher, you really need to do a summer internship in banking - if you don't, you're going to have a very tough time securing a full-time offer from a bank no matter what school you go to.
INSEAD is really geared towards those who want to work in Europe (or Asia if they decide to end their term on the Singapore campus).
Yes, INSEAD is a great school, but it's not really going to suit your needs.
As for investment banking and age - it can be an issue, but it's a matter of showing that you're committed to the job. In other words, you have to convince them that at 33-37 (3-4 years as an associate), you're willing to get slapped around and be as subservient as someone who may be 5-8 years younger than you. And some bankers will either accept you for it, or will look down on you for it because you're willing to do it at your age. Also, some folks may simply not feel as comfortable managing you because of your age -- they feel more comfortable grinding a 26 or 27 year old single dude than someone in his 30s.
As for private equity, if you want in, you really have to do banking first - there were folks who have gone directly to PE in the past during the bubble/boom years but unlikely now and in the future as the sector becomes less frothy. The other way is if you have access to money (i.e. you come from a very well-to-do family that has contacts with other very rich people -- remember that PE funds aren't just about investing money, but raising money as well). "Operational knowledge" is a commodity - if you want to do real estate PE, chances are your skillset and knowledge isn't particularly unique. What is more valuable is CONTACTS that lead to deal flow and money. If you do have that because of your family or your personal network, then sure some real estate PE firms may be interested in you.