Your characters in the Library pod can not use/equip weapons so you don't need to take strong offensive characters with you on this run.
I recommend taking Josh and Max to start. Josh gets high wit and gives a great bonus if you have him operating which he can do right away with the starting items you begin with. He also unlocks it naturally at level 3.
Spend the first few floors mostly focusing on science modules, build 2 of the first floor and have Josh operate to boost your income while using Max for door opening.
You can pretty much do the entire run using only Tesla's as your offensive weapon mixed with Neurostuns, so get those upgraded as soon as possible. Tesla guns focus on anti major module monsters so it's very beneficial once the Dozers and Zoners start showing up. Neurostun slows monster movements and they stack, so the more you have in a room the slower they will move.
Since your characters are weak you will be doing a lot of falling back when opening a door to lead the enemy to your minor modules instead of fighting them head on.
After a few floors you can pretty much stop bothering with science modules as you should have the few things upgraded that you need. After that, alternate between Industry and Food as you see fit. Josh gains wit every few levels and will increase the amount his operate bonus will give, he is also good to keep in a room that gets a lot of enemy waves as his Overclocked skill helps minor modules. (Minor Modules in room): Attack Power +50% (lvl 1) +75% (lvl 2) +100% (lvl 3)
Max is your primary door opener, his Pilfer skill gets bonus dust when entering a room that gives dust. So at level 15 you get +3 Pilfer which when opening a door that gives you 5 dust, you get an additional +3. Pretty handy in the late game.
I recommend keeping an eye out for other good operate characters during your run to recruit to help boost your income. Those who have operate aside from Josh are Op Bot, Elise, Rakya, Golgy, Warden Mormish, Deena, Hikensha and Kreyang.
The Science pod has more minor and major module slots over other pods giving you plenty of places to build.
Lastly, you may want to also research LAN Module if you're having issues with your mods being destroyed to quickly as it gives minor modules a bonus to defense. It applies to all mods on the floor and doesn't need to be built in any specific room.
Also it's good to have Emergency generator researched, you most likely will rarely need them or not at all but they can help if you get a poorly set up floor or lack of dust income. They are expensive though so keep an eye on your industry.
If you're worried about dust in the late game as well, building the store module can help. Once you find a merchant, if you have a store built he will teleport to that store and you can have someone operate on that module. Operating on a store module that has a merchant will give you dust per door. It's good to have a high wit person on this to maximize the income. It also stacks so if you find multiple merchants and want to build multiple stores to then operate for even more dust, feel free!