After conquering The Candlelit Sanctum, can I do the Candlelit's conquer effect, and then decide whether or not I want to use Rek'sai Void Burrower's conquer effect? Or do I have to declare that I'm using both effects?

No, you cannot resolve The Candlelit Sanctum's conquer effect and then decide whether or not to use Rek'Sai, Void Burrower's conquer effect. You must commit to all triggered abilities at the start of the sequence.

According to Rule 383.3.d, when multiple triggered abilities you control are triggered simultaneously, you must choose the order in which they are placed on the chain. You must declare your intent to use all triggered abilities you wish to resolve at the start of the sequence.

Correct Sequence of Operations

1. Conquer: The showdown concludes, you gain 1 victory point, and both "When you conquer" triggers (The Candlelit Sanctum and Rek'Sai, Void Burrower) activate simultaneously.
2. Declare: As the controller of both triggers, you must declare that you are using both and select their order on the chain.
   • Example: You declare "Chain 1: Rek'Sai's ability, Chain 2: Candlelit Sanctum's effect."
3. Finalize: You must pay any costs required to place these triggers on the chain.
4. Resolve: The items on the chain resolve in reverse order (Last In, First Out).
   • Step 1: The Candlelit Sanctum's effect resolves first.
   • Step 2: Rek'Sai's ability resolves. At this point, you make the choices associated with the ability (such as which cards to reveal and whether or not to play one).

Important Clarifications

• "May" Abilities: If an ability contains the word "you may," you must decide whether or not to place it on the chain at the moment the trigger occurs (Rule 383.3.f, FAQ #11007). You cannot trigger it, wait to see the results of another chain item, and then decide to add it later.
• Costs: As established in FAQ #10344, even if you resolve the Sanctum effect first, you must still pay the full Energy and Power costs for any card you choose to play via Rek'Sai's ability, as the ability does not grant a cost reduction.

In summary, you must commit to all effects at the start; you cannot selectively choose to use a trigger based on the outcome of another.

Note: I could not fully verify the mandatory status of Rek'Sai, Void Burrower's ability against the retrieved rules.