Thanks for the pair of questions
For Antoine, his ability reads: React: After Antoine enters play, search your discard pile for an action card that starts a job and put it into your hand. Discard a card. You may unboot your dude at home and give them 2 bounty.
The unboot in the last clause is completely optional (specified by the you may unboot), and the bounty giving is not dependent on you having to unboot that dude. Were that the case, the card's clause would read as: you may unboot your dude to give them 2 bounty. Notice the "to" in there instead of the "and".
For the second question regarding the goods, it's ability reads: Noon: Ace this card to search your discard pile for an action card that starts a job marking a location. Play the card, making this dude the leader if able. While leading the job, this dude has +1 bullets and is a stud.
While it does not have the reminder text, the costs of the card must still be payed for you to play the card. We can verify this by the first paragraph in the FAQ regarding 'Help Text'
Italic card text in parentheses is called “help text.” It does not change the way the card works, but serves as a reminder of rules that apply to the card, and is intended to help new players learn the game.
Lastly, bear in mind that De Annulos Mysteriis only searches for jobs that mark locations. So this would make Ambush an ineligible target to search for.