Zin's ultimate bots guide

Yes, Sienna is a better bot than Bardin. She is almost as durable as him, while unlike him, she is also quite good at killing and can heal the entire team.
If you want your bots to be better at killing Specials you can trade Warrior Priest of Sigmar for Zealot.

These for everyone (except a small change for Victor's Trinket).
Necklace:
(Barkskin is the best, you should use it too)
Charm:
(Attack Speed is very important for bots because if it is low they just don't attack and Power vs Skaven because Skaven are the most common enemies and in some missions there are even only them - it is Vermintide after all)
Trinket - If you want grims:
(Cooldown is better than Stamina, yes)
Trinket - If you do not want grims (use this for WP always):
Trinket for Zealot (no matter grims or not):
(Zealot doesn't need health, so he doesn't need Curse Resistance, and his defense is offense, hence Crit Chance)

I like to use Sienna's Mace and Fireball Staff. She's great with them and their Feuerbach illusions suit her quite well too. But she's equally good with Flaming Flail and Bolt Staff so it's up to you.
If you want to make her one-sidedly focused on killing armored elites, give her Crowbill - I finished Cata Convocation of Decay this way for the first time because the concentration of Chaos Warriors used to be insane there.

The Ironbreaker bot is good with any melee weapon, but if you want to make him really sturdy while still keeping his ability to kill Specials, give him Axe and Shield. (because bots often refuse to use ranged weapons against Specials)
As a firearm, Handgun is the most versatile. But if you want Bardin to help you with Monsters and Patrols, give him Trollhammer. And if you want to play Deed without Ammo, Drakefire Pistols will be the best.

For WP use Hammer and Shield or just Hammer. Personally I use 1h Hammer for him, because he looks the most lore friendly with it.
If you want Zealot to be better at killing Specials (at the expense of effectiveness against Hordes) give him Axe. If you want more durability choose Dual Hammers. And for ranged - with Brace of Pistols, the Zealot bot is better than most players.

Mercenary is the least durable bot and will be dying the most, but he is slightly better at survivability if you give him Spear and Shield. He's also surprisingly capable with Greatsword.
As a firearm give him Repeater (or normal) Handgun. Kruber is a pretty good sniper.

This is the most important section of this guide (much more important than equipping your bots). There are rules:

1. Stay with your team. This rule applies whether you're playing with bots or with players, and it's the most important rule in the entire game. (breaking this rule (often by elves) usually leads to a failed mission) Always wait for your mates before going beyond the point of no return!
2. Monsters (and Lords) are the biggest threat. Kill them as fast as possible. Use bombs and potions unless you are playing a char that is good at Monster slaying. (this is different when playing with players where everyone has a role in the team)
3. Bots often use melee weapons to fight Specials. Expect it and try to kill the Specials yourself. If for some reason you can't shoot the Special yourself, at least try to look at it and go in its direction - then there is a better chance that the bots will take care of it. Also, bots often only become aware of Hook Rats and Leeches when someone is immobilized - prepare for it.
   Warpfire Throwers are the doom of the bots. Kill it fast.
4. If you have more healing items than you need, heal those carrying grims if you don't want to lose them.
5. Give bots Tomes in this order: Ironbreaker, Warrior Priest of Sigmar / Zealot, Mercenary, Unchained
6. Give bots Grimoires in this order: Ironbreaker, Warrior Priest of Sigmar / Zealot, Unchained

A little bonus at the end. I like it when the whole team is stylish and looks uniform. Here are my tips for a red and black team theme and goldenish frames: