Just thinking out loud again.
If individually-purchased stocks interest you, some banks will have a minimum charge ($40-$50) for buying and selling stocks if you keep a certain balance with them. For instance, our bank, (BOA) requires a min. balance of $10,000, inclusive savings, checking, and Money market accounts, to be eligible for buying/selling stocks at a low one time fee. DOn't forget to set some of the money aside from selling stocks, to pay the capital gains tax at the end of the tax year.
Also, rather than tying up money in a savings account, consider opening a Money Market account, the interest rate is usually 2% higher than a savings account, although you are usally limited to minimum amount that you can withdraw at one time (BOA minimum withdrawl amount is $500) But usually if you're tapping into a savings account, its usually for a big ticket item, so meeting the minimum is not a problem.