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There are options boards at:

You pay the cost of the contract(s) up front, then at the expiration date of the contract either allow the contract to expire (and lose only the cost of the contract) or exercise the option and buy the stock at the designated price. You may then either continue to hold the stock or you can sell it immediately and pocket the difference between the contract price and the current price. Right?

Right. If you don't want the stock you usually sell the option on expiration day if you can get a reasonable price for the option, so you only get charged one commission (sale of option) rather than two (exercise of option + sale of stock). In fact due to "time value" of the option this is almost always best.

Option price is made up of two components: "intrinsic value", the difference between the exercise price and the current stock price, and "time value" representing potential additional appreciation in the future. As time goes by the time value gets less and less ("decays") not quite linearly.

Is the benefit of simple call or put options as described above simply the ability to control a large block of stock with less money?

No. Although options can provide leverage (which is good if you guess right and bad if you guess wrong) you can also get it by buying on margin. An option allows you to get a higher level of margin...if you guess right on the strike price. If you guess wrong you end up controlling zero stock for your money.

Plus, if you're right and the stock does rise and you want to exercise the option, you have to come up with that big block of money to buy the stock anyway.

In this case you'd just sell the option, collecting the entire intrinsic value (profit) plus any remaining time value. Very few options are actually exercised.

the terms are confusing. There are 4 options,

These terms are well-defined in many places. If you dive into options without understanding them you are sure to lose your shirt. There are good reasons why there are barriers to entry when trading options.

Remember: If you buy an option, you most likely WILL lose YOUR ENTIRE INVESTMENT.
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