Learn English – “Put a knife to/at/on throat” – which one is preferred

I'm a native speaker, and we use "get ready" in exactly the way you describe.

Even though we sometimes qualify the phrase by saying: Get ready for [some event], that "for" clause can be omitted when the listener already knows where we are going. In other words, although get ready can mean different things in different contexts, I can still usually say:

C'mon! We're leaving! You need to get ready!

and that will be understood to mean: put your shoes on, brush your teeth, comb your hair and look presentable, etc.

The precise meaning get ready will vary, depending on where we are going. So long as the hearer knows where we are going, I don't need to add the, say, for your piano practice. For example, I have teenagers at home, so, for me, it works very much like this:

10 or 15 years ago, though, whenever I said, "Let's get ready" to my wife, that always included "Make sure we have the diaper bag!"

You needn't worry about get ready being misconstrued to mean "brace yourself for some bad news" or "get into your starting blocks." Those are very specialized meanings that people wouldn't even think about, unless they were in a situation where that would be the meaning that makes the most sense.

For example, if you wanted your picture taken, and I was holding your camera, I might say, "Get ready..." – which doesn't mean, "go put on your shoes," or, "brace yourself for some bad news." It simply means, "Get ready, I'm going to snap the picture now" – so you should probably just give me your best smile.

Wait a minute

This is pretty generic and informal and is often used idiomatically to ask someone to pause what they're doing until told to continue. It doesn't usually mean exactly a minute, any more than "wait a second" means exactly a second.

Wait for a minute

This sounds like something that you'd find in directions/instructions:

Wait for a minute and then add the oil to the pan.

In this case, it more often means exactly a minute, though it's not required. The exact timing here is more important. You would be unlikely to find native speakers who would use this in the idiomatic manner of the previous example.

Now, does this carry over to numbers of minutes greater than one? Sort of?

Wait five minutes

Will usually mean five actual minutes... otherwise, why bother specifying the number. As mentioned before, "wait a minute" doesn't really mean a minute... one could end up waiting for a few seconds or several minutes in the end. Even in directions, you'll often find they've left out the "for" in this case:

"Remove from stove after one minute of boiling and wait five minutes before topping with granola."

So what about with the "for"?

Wait for five minutes

This isn't wrong. Using it this way is not ungrammatical at all, it's your choice. It's not required and you will definitely find examples of it, particularly in more professionally-written instructions:

Slide the whole skillet under the broiler, and wait for five minutes, until the crumbs are golden brown and the salmon is done.

This is also discussed, though not to a great degree, in Cambridge Dictionaries Online:

Wait means ‘stay in the same place or not do something until something else happens’. We can use it with or without for:

• Put a tea bag into the cup, then add water and wait (for) a minute or two before taking it out.
• I phoned the head office but I had to wait (for) five minutes before I spoke to anyone.