The solution to both is investing in stock index funds and ETFs. While mutual funds might require a $1,000 minimum or more, index fund minimums tend to be lower (and ETFs are purchased for a share price that could be lower still). Two brokers, Fidelity and Charles Schwab, offer index funds with no minimum at all. Index funds also cure the diversification issue because they hold many different stocks within a single fund.
“I know stocks can be a great investment, but I’d like someone to manage the process for me.” You may be a good candidate for a robo-advisor, a service that offers low-cost investment management. Virtually all of the major brokerage firms offer these services, which invest your money for you based on your specific goals. See our top picks for robo-advisors.