So does it make sense to send a small amount first, confirm that they receive it, and then send the rest?
Because I have also heard that each address should not be used more than once.
I do practice sending small amount first especially after long period of inactivity at the given exchange just to be sure they have no technical issue to process my transfer. Regarding reuse of address, if your second transfer is really big, IMO, it's better to send to address already drilled by first transaction to eliminate any hypothetically possible flaw that may appear in the course of new address generation.