This question has a lot of answers. Depending on the brokerage house it can be a minimum of $2,500 or more. There is a minimum set by the SEC, but brokers are allowed to raise the minimum to protect themselves if they chose. Most do not do this unless the markets are crashing.
As for a singly naked long option.....this can get expensive, which is why most people are spreading the risk off by doing vertical spreads. From there traders can go even deeper into reducing costs by spreading the initial cost off (say a vertical spread) off by selling another spread against it (condor, butterfly etc.).
I have had many instances where I have bought $5,000 of vertical spreads, hedged them off later by selling another spread against it, and reduced my risk to $100. From there I have sold some at a profit and had $0 invested in a trade. This requires a lot of work and dedication to learn, but when you can take $5k of risk and reduce it to $100, what is the problem?
How long does it take to make that $5k at a real job? Do this several times a year and it is a no question that spending a hundred hours learning this is better than spending 100 hours watching TV.
While getting started find a GREAT mentor or read all you can. There are a lot of sites that teach option basics for free. I have my own personal favorite, but that is because I have been doing this for YEARS and am at a more sophisticated level, and I need a company that is full or REAL floor traders as a platform to learn from. But even they have some free material, but most is NOT basics, and not applicable to you.
You can get a lot of good FREE material on the CBOE (Chicago board options exchange) site
http://www.cboe.com/LearnCenter/courses.aspx. Also I have found that the company I prefer for paid education has free info on their Facebook page and website which is nice. I hate nothing more than being sucked into so-called free and then being pounded by sales pitches for $10k in materials later.
I hope this helps.