Overview
Jenny is a quintessential Flex, which means she is there to keep her team safe and on task. Often times, your ability to handle issues in a multitude of ways will be the only thing keeping the team going.
At first, you should be mulligaining for lucky cig case, as well streetwise and physical training. A weapon is nice, but not as critical as getting your primary tools for passing tests or getting through your deck faster.
Don't underestimate your evasion and how critical it can be. Often monsters will threaten to ruin your team's day not because they need to die, but because your buddy needs to be able to take a turn without eating 3 attacks, so any time someone can't kill a monster, you should consider going there and bamboozling it, especially after your deck gets upgraded a bit. But you also can help contribute to kills. Likewise, your more independent and better able to track down clues in out of the way spots, so if your team is rolling deep and plenty safe it might fall to you to rush to some weirdo area to cluesearch.
Ultimately your main goals as a flex are, in order: Keep the team safe, be in a position where no one needs to drop anything to help you, and then tackle objectives other people would need to waste time to handle.
Upgrades
Upgrade wise Jenny has a lot of good options, but your first priority is to upgrade Streetwise. Always starting with streetwise means your set to protect your entire team from a big monster or start slurping up clues on turn 0. After that make sure to upgrade your lucky cig case, being able to search your deck almost every turn is truly a fantastic effect. Finally, making sure lockpicks are upgraded is a big deal. Level 0 lockpicks are questionable in Jenny, but serviceable, but for just 2 XP you can be darn sure you will keep them for most of the game.
Depending on how you want to specialize further upgrades will vary: If your team has a dedicated monster hunter you can focus more on the clue gathering tools, such as Skeleton Key and Lola. Conversely Delilah and the .25 automatic are fantastic monster hunting tools if your combatants need help, and if you really want to break the bank you can get an even more magical sword... club thing... in the form of Timeworn Brand!
Ultimately you are free to mix and match, and often times you will be doing 'what needs done' rather than focusing on one specific thing. Either way, one upgrade you will want to consider if your running a lot of interference evading enemies to 'tank' or using evasion to just keep yourself safe while poking away at clue spots, is Pickpocketing, which allows you to gain a truly insane amount of cards and resources off evading enemies in combination with Lucky Cig Case, Watch This, and Quick Thinking and works extremely well with almost any strategy.
Some filler upgrades include Another Day Another Dollar, as well as Hot Streak. More money never hurt anybody, and while these are not critical for this rendition of Jenny making your economy run smoother is a great way to spend the last of your XP during a campaign.
About:
This is part of a series of decks I made for teaching Arkham, and is probably the 'best' one for a player who is familiar with cardgames or RPGs to pilot. This deck prioritizes being easy to pilot, not including wacky concepts or archetypes like running some sleight of hand nonsense, not using any taboo cards that were too severely tabooed, and showing off how cool Arkham can be, because a deck being easy doesn't mean you can't make it awesome.
And what is more awesome than being a chain smoking single gal in the 1920s running around wearing track shoes with her pearls and fancy dress, stabbing ghouls in the face with a magical god damn sword?
On a related note, this is not an optimized deck. It will most certainly get you through Dunwitch and Carcosa normal (And maybe TCU if you are tenacious!), but some compromises were made in order to maximize the experience of playing your first campaign of Arkham. It avoids certain strategies that hyper-focus the deck too much or trivializes certain challenges, and prioritizes cards that are fun to play (though still serviceable) that help play up the fantasy the deck tries to capitalize on. It also prioritizes making sure the player using it doesn't get womped by anything too hard, which can make new players a bit reluctant to show the tenacity one needs to tackle the challenges Arkham can throw at you.
While many veteran players favor heavily specialized decks, the fact it is a flex helps it slot more seamlessly into more team compositions, making it easier and safer to just hand to a player looking to play, perhaps a new player curious about the game at a store's game night, or someone who wants to take a guest spot in a campaign,
Ultimately, it is meant to be a set of safe hands you can put a new player in, either as a group learning game, or for one player on a team who is new, to ensure they can always contribute and always keep themselves safe while still being an 'honest' deck that actually plays the game of Arkham.