Standardized tests: Which ones? When? How many times?
The answers to these questions vary radically from student to student. Anyone who tells you there's one right answer for everyone isn't as knowledgeable about the tests as they should be! There's no way to thoroughly respond in this format, so I'll just provide a few guidelines.
All students should take a full-length practice SAT and ACT before deciding which one to pursue. The PSAT or PLAN is not an acceptable guide since these tests are truncated versions of the real thing. Having the full experience of each test (in all it's exhausting, mind-tangling glory) is essential for making an informed decision. Other factors may include available test accommodations for students with disabilities, preferred test dates/centers and access to prep materials. Most students develop a clear preference for one or the other, so when you know which one is for you, stick with it! Many students think they need to take both tests, but I disagree. The SAT and ACT are very different animals and it can be confusing to prep for both, not to mention a giant time-suck in your already busy schedule!
As for when to take your test of choice, the only guideline is to allow ample time to retake it at least once before applications are due in the fall/winter of your senior year. In general, you should take it for the first time no later than May/June of your junior year. But if you prefer to get it out of the way earlier, please do! If you have plenty of time to devote to preparation the summer after your sophomore year, do it. Then take the test in the fall while the information is still fresh. Be sure to also plan for AP exams and SAT subject tests if they're on your agenda.
The answer to the last question is a little easier to answer. If you're applying to a selective school, many (most?) require you to submit all of your test scores from the SAT or ACT. A general guideline is to take the test no more than three times, unless you have a very good reason for doing so. More attempts implies that you're hoping luck is going to shine down on you rather than putting in sufficient preparation before test day. Each time you take the test should be "for real," with you putting in your best effort. Don't use a real exam for practice...that's what prep materials are for!
Hope that gets you thinking about a plan. I recommend talking to a test prep pro to discuss your specific needs, especially if you're intending to apply for testing accommodations. Good luck!