Is it better to send 10,000 coins for staking in increments of 1000 or one 10,000 transaction for best results?
Depends on the coin.
Most older PoS coins, use coin weight , so the more weight per block the faster you can stake.
Others place max cap limits per stake, so it limits the amount you would want per block.
Devil is in the details / specs , post which Proof of Stake coin to get an answer to your question.
FYI:
Also Post your Goal
Is your Goal to stake as fast as possible to earn the max compound interest?
or
Is your Goal to help secure the network?
The Answer changes depending on your goal.