Too many start-ups don't do the research and totally just go straight to development. Mine included. Ie. http://www.plentyoftweeps.com
In anycase another startup I had I waited 5 years, craigslist.org had been operating that whole time and basically dominated in the markets where they had that 5 year run time, so I had to squeek by and penetrate markets where craigslist.org wasn't.
Anyway start ASAP with the market research. Ask people on buses, at restaurants, in planes, family and friends if they would use your service/product.
In addition, I would say, as soon as you see a need (but, validated through market research, formal or informal) go after it. There are lots of intelligent people thinking out there, who are as capable as seeing market needs as you or me or the next person. The only thing that matters in these days of open source and low cost startups is execution - who comes first to the market with the better product.
A need that is not met can be a current $0 dollar idea but if developed well can be a future million dollar idea. If you hit on a million dollar idea when you are poor, thats how you would get rich!
Before/during/after college? - 'Now' would be best.
I feel like I've missed the target on the second one way more then the first. One of my first projects launched well and had some good stable income (about $1500/month). After that I decided to think big, and now I have a few projects that are just too big for me to do in my spare time. I think some thought should be put into how long it will take you to get to the minimal viable product.
He discusses the elements you need to create a successful startup. To answer your question of "when" to start a startup, it may be worth considering these elements. When you have them (or 2 out of 3 of them since the third element is to spend as little money as possible, and you can't really do that until you're in it) it may be time.
Another relevant pg essay: http://www.paulgraham.com/notnot.html
Here he discusses some of the dimensions you include in your question (age, wealth, in/out of college) and analyses their impact on one's decision to start (or not start) a startup.