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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.
If you want to learn more about how to invest in a stock, check out the directory of Investing for Beginners articles I've written, sorted by topic or head over to my blog for more esoteric and advanced topics that aren't particularly appropriate for beginners. Whatever happens, remember that stocks are just one of many types of assets that you can use to build wealth and become financially independent. 
Prior to investing in a managed portfolio, E*TRADE Capital Management will obtain important information about your financial situation and risk tolerances and provide you with a detailed investment proposal, investment advisory agreement, and wrap fee programs brochure. These documents contain important information that should be read carefully before enrolling in a managed account program. Please read the E*TRADE Wrap Fee Programs Brochure for more information on the advisory fee, rebalancing methodologies, portfolio management, affiliations, and services offered.
Momentum investing usually involves a strict set of rules based on technical indicators that dictate market entry and exit points for particular securities. Momentum investors sometimes use two longer-term moving averages, one a bit shorter than the other, for trading signals. Some use 50-day and 200-day moving averages, for example. The 50-day crossing above the 200-day creates a buy signal. A 50-day crossing back below the 200-day creates a sell signal. A few momentum investors prefer to use even longer-term moving averages for signaling purposes.