If you want to trade stocks actively, you should open an account with a direct access broker. Since over the last few years I have practically stopped trading stocks in favor of currencies, I can’t really recommend any broker in this category.
If you are willing to give currencies a try (and I think you definitely should), you can get access to a free simulator from my website. The simulator (or “demo” as it is often called in the Forex world) works with live market prices while you practice with fictitious money. It is a great learning tool. After you practice with the demo, if you are ready to trade live, you can open an account with my preferred FX broker in this section. The minimum to open an account is $250 USD.
With this account you will be able to trade different lot sizes (standard lots = 100,000 units of the base currency, mini lots = 0.1 lots = 10,000 units of the traded currency, and micro lots = 0.01 lots = 1,000 units of the traded currency). This flexibility and ability to trade very small amounts means that you can learn how to trade while sometimes risking pennies.
This is great for new traders that don’t have a lot of risk capital and also for others who just want to kick the tires a bit without betting the form. If at the end of the day you don’t want to pull the trigger yourself, the trading robot or AutoTrade program might be a good fit for you. It will let you participate in active trading without having to make the decisions to buy and sell yourself.