We normally have a rule when we’re playing with more than 3 people that you must have your purchases ready for when your turn starts, or you don’t get to buy. I often am throwing my purchase onto the mobilize units boxes in the bottom corners directly after my opponent does.
Obviously, you like to hide them most of the time, and we usually keep our purchase choices hidden directly behind our boxes, where the opponents sitting on the other side o the table can’t see them.
But if you’re up next, then your purchases normally don’t impact what your opponent is doing, especially after he’s already decided his buy. If it’s a drastic buy, you keep it to the side, but as Russia, India, China & ANZAC have very basic buys (France none at all), showing stacks of infantry and artillery aren’t going to give him much to go on. Besides, he’s already made his purchases :)
Even America and Great Britain it isn’t necessary to hide. Ships and planes is what you expect, so yeah.
Minor changes are allowed, because if India was planning on buying tons of infantry, but Japan is positioned to sacrifice transports, some subs might be thrown into the purchase, or America might go for some destroyers if Italy goes sub-heavy.