Jessica Drew has had it tough, being named after a legend in Marvel comics. She’s constantly sexualized. She goes through more outfits (to be fair, they ROCK), but it’s ridiculous.
There’s the classic 
.
the
spidey derived,
the 
venom,
the spider-gwen which is, I guess,
,
and even the newer, less skanky
. Do a google image search on Spider-Woman costume change marvel comics. Here.Spider Woman outfits - Google Search
Of all the covers, and there are a CRAP TON of them, I think this one works best. It’s Spider-Woman, but without immediate emphasis on boobs, butt, or spread eagle. I mean, at that rate, she’d be better served with a name change to Major TnA. Because That’s how Marvel draws her. She’s the skankiest drawn character in Marvel.
But she’s cool.
So I suggest
Spider-Woman. Probably the classic costume. http://static.comicvine.com/uploads/scale_small/0/4/19940-2960-22245-1-spider-woman.jpg though this one http://upload.wikimedia.org/wikipedia/en/2/23/Ultimate_SpiderMan_98_cover.jpg is just killer.
8750 HPs.
Venom Blast. 9 AP.
Spider-Woman’s body naturally generates venom, which she uses to launch a concussive blast. Stun an enemy one turn and deal 350 damage.
Rank 2. Stun duration increased to 2 turns.
Rank 3. Remove damage but stun enemy team 2 turns.
Rank 4. Stun removed. Damage increased to 600.
Rank 5. Damage dealt increased to 900, and to the team instead. Stun her one turn.
Why remove the stun, right? Spider-Woman has shown that she can vary her Venom Blast depending on her target or targets. So the build you go for is determined by her company as well as who you want her to be.
Because I said so. PASSIVE.
Spider-Woman’s phermones warp your senses to her benefit. Whenever the enemy attacks Spider-Woman, she generates one 
tile of strength 20.
Rank 2. tile strength increased to 50.
Rank 3. Generate 2
tiles of strength 50.
Rank 4. Generate 1 
tile of strength 50.
Rank 5. Generate 2
tiles of strength 50.
Again with the dichotomy. I want you to build her based on how you see her working out. And that means multiple viable builds. This is the way to have built Falcon.
Double Agent of S.H.I.E.L.D. 10 AP.
Spider-Woman goes deep cover to decipher the enemy plans. Steal all enemy AP by 2.
Rank 2. AP steal increased to 3.
Rank 3. Place a 3 turn timer tile. (bomb). destroy 3x3 grid.
Rank 4. timer decreased to 2 turns.
Rank 5. Place a second timer tile.