Sweating the Small Stuff

Let's take a look at your basic Amber character. She's Real when everything and everyone else in the universe is Shadow. She has the power to travel worlds or shape them to her liking. She's better at everything than the foremost expert who ever lived. She's effectively immortal.
This is not the kind of person who worries about whether she's carrying fifty feet of rope.
As a system, Amber takes care of all the little stuff. Attributes are general enough to apply everywhere and any Power can probably solve 99% of your day-to-day problems. The only significant threats to your character are your siblings, and they're more than dangerous enough to merit your full attention. So give it to them. If it's less important than a treacherous demigod, it isn't worth your time.

Don't Quantify Everything

The most frustrated player in Amber is the one who asks the question, "How much?" Amber isn't a set of actuarial tables; there isn't any super-secret GM handbook with how many pounds 4th rank Strength can lift or how many beers 2nd rank Endurance can drink and stay sober. Thinking that way is an ingrained habit in most roleplayers because almost every game in existence encourages you to do so, but it's actually a hindrance here.
In 99% of cases the GM won't have considered whether or not you can do something until you ask, and most of the time they're going to give you an answer like "You can try" or "Probably." There are no hard cutoffs for stats where you must have Rank X to be able to accomplish Feat Y; the GM evaluates every situation individually based on context. If you fail it's because the GM didn't think you had a reasonable chance to succeed in that case.
As such, your ability to do something changes from moment to moment depending on the situation-- even though your stats never change. You can fail tasks that you successfully completed before and succeed at tasks that you'd previously failed if the circumstances are sufficiently different. You can't rely solely on the numbers; high ranks make things easier but they're never a guarantee.
On the flip side, low ranks don't necessarily prevent you from doing difficult things. If you approach a problem correctly you can usually succeed regardless of your stats. Ranks are good, but creativity is at least as important.

Understanding Death, and Embracing the Curse

Chances are at some point in everyone's Throne War career, they'll die. For some, that comes sooner rather than later and it can get you down. You (probably) won't be king now, and that sucks. But after you have died a whole new world is open to you, and in that world the living are not safe. You get your Blood Curse unleashed with righteous and vengeful fury, and boy is that FUN. You job now is make the lives of living just that much more of a hell, and even get them to join you if possible. Even though you can't be King, rest assured that you can still effect the Throne War!
The flip side of this coin is the Murderer. Some people really don't want to die, and that can be hard. Don't be a dick about it, and make sure there are no hard feelings out of character even if you feel you are doing everything right. Expect to be Blood Cursed though, and be ready for those consequences.
A common level of courtesy is expected from siblings, and it is strongly encouraged that you not kill anyone during the first playblock. Mortal wounds, outright theft of Toys/Plot Stuff, mental domination, and Primal Forms are all fair game and definitely encouraged! Keep in mind that new Players are especially protected by this custom, except from the wrath of the other newbies...