Most 401k or IRA plans can let you choose how you want to invest, usually at least one or more fairly diverse funds that can be comparable to index funds, more conservative or more aggressive. Personally I like the ones with funds geared towards people retiring in 10, 20, 30 or 40 years - this is an indication of the risks and potential rewards. The reason you should be maxing out your 401k and/or IRAs before thinking of a normal brokerage account is because you typically will be investing pre-tax dollars which gives you quite the leg up on the investment potential. Of course if you just want to learn about stocks trading individual companies can be fun as well, but don't think you'll actually turn a profit unless you've got a lot to invest. Then again you may get lucky or discover you're good at picking winners, but only invest what you can afford to lose.
If you can change your contributions at will (some companies only allow a change at a special time of year) now may be a good time to up them - but try not to reduce them when the market recovers.