Most plants readily available are easy care and aren't touchy at all. Doing what BK suggests is the way to go. Watch the temperature that you don't shock them, and they'll be fine -- with some exceptions. As Jenn said, Hornwort will almost always shed.. with some plants, the leaves are going to die back and regrow. This is normal.. just how those plants are.
Others considered to be "difficult to grow" are very sensitive to sudden water changes, particularly pH and hardness. Take one of these that's used to growing in soft water/low pH and plop it into a new tank with hard water/high pH, and it's a goner. This plant can never survive that. That's part of the reason why an otherwise easy plant might get that reputation for being so difficult to begin with. It needs time to transition over but most people didn't know it.
I read about one plant where people commented that it just doesn't grow, it always melts, don't ever buy this plant, it's not really aquatic, and so on. There were lots of reports online in different places where they complained about the vendor selling them because of this. Many people thought it was a complete rip-off. Then I found a discussion at one site that explained why -- in order to transfer that plant successfully, you have to match the water exactly. For this one, if you take it out of the bag, rinse it abruptly under tap water, and then place it into your tank... it's going to melt before your eyes every time.
Basically.. get an idea what the basic care requirements are for plants before you buy them. At least so you'll get the light requirements and other general conditions right. And if you're getting something you already know is rare, hard to find, really expensive, or difficult to grow.. those are the ones that take a little research first. Any reputable seller of plants who gets an email from you asking about it's requirements or the conditions it's currently growing in will be happy to answer all your questions. If they're not, don't buy from them.