Between scholarships, working, and living fairly frugally, I graduated with a very little debt (less than $3,000) but also no money. That first paycheck came in with days to spare.
My biggest financial mistake was gambling too much money on a compete flyer of a stock right out of school. First it doubled, then it went to zero. That cost me more money than I should have been willing to lose, but also turned me off of investing. Unless you count buying a house that was a bit of a fixer upper and contributing to my 401k, I didn't start investing seriously until about a year ago. Fortunately that meant I had tons of cash to play with, but it also means I missed out on a pretty great run up over the last 8 years.
For my goals, I've decided on a mix of diversified dividend income funds, yield stocks, and risky growth stocks with the last two categories focused on an industry in which I have an information advantage. I know things about the underlying industry that are hard for even a well-connected New Yorker to replicate, I also spend a lot of time trying to figure out how the funds think about things, and I can move faster. So far it has served me well; I've outperformed the sector and broader market dramatically over the last year.
When planning for retirement, I ignore my 401k, pension, SS, and Roth IRA for several reasons. The 401k and IRA are loaded with low risk funds, so by treating my brokerage accounts like they need to get me to my retirement goal by an early age it pushes me into taking on higher risk/return investments... I want that. Second, the 401k, SS, IRA, and pension won't be available until long after i intend to be able to retire anyway, so it makes sense to treat them like a fallback option/safety margin. Last, i believe there is a high probability that I'll end up losing some or all of my SS due to benefit reduction and means testing.
TL;DR
1. Don't do anything too stupid
2. Know your goals
3. Build a safety margin into everything
4. Diversification means giving yourself a sturdy base AND upside, not simply spreading your money across a bunch of funds that all do the same thing
5. If you choose to invest in individual stocks, pick a specialty to understand really well. You can't be an expert in everything and if you try you'll eventually get pantsed. You'll still get pantsed, but hopefully less often.