Ty_Cath

Guide: https://www.visajourney.com/content/i130guide2
The G-325A in your list hasn't been used in a couple years.
 
First step is to confirm that her J-1 does not have a 2 year home residency requirement. If so, that either needs to be waited out abroad OR she can apply for a waiver and hope for approval.
 
ETA for work permit (EAD) and travel permit (AP) is ~4-7 months right now. Who knows what that will be in ~May. Don't make any firm plans until they are in hand. Leaving the US without AP abandons the AOS process.
 
There is no "fast lane". The process is neither easy, cheap, nor fast. Buckle up for the long ride.
Keep in mind ROC in 2 years after getting the green card.
Then (optionally) naturalization afterwards.

Yes. The I-130 packet is a petition to establish the legal relationship between petitioner and beneficiary for the purposes of being eligible for an immigrant visa.
The I-485 is the application to adjust status to permanent resident within the US. This requires an underlying immigrant visa petition.
They are separate packets, although you qualify to file them together as the US citizen spouse. It is possible for only the I-130 to be approved and I-485 denied (i.e. if the beneficiary leaves the US without AP). Then the I-130 proceeds normally and consular processing abroad for an immigrant visa would continue instead of doing AOS within the US.
 
Those are timelines from well over a year or 2 ago. Expect 4-7 months now.
 
Expedites and emergency AP are available, but they are only granted on a case by case basis for emergencies. It is absolutely not something to rely on, and requires considerable supporting evidence. People have been denied this to attend funerals for close family members.

@geowrian got you all the info you need on the forms and what to do with them (and the J1 residency concern), so I'll address your "proof of bona fide marriage" questions. 
 
That's fine, not everyone likes to take pictures. We're not photo people either, and we submitted none. I was worried at the time, but keep in mind--pictures are secondary evidence. They can be faked, anyone can smile in photos. They're not the best kind of evidence to have, it's secondary evidence. 
 
I recommend pet insurance (I was thankful when my dog got diagnosed with bladder stones. Things will go awry when they get older.) I included pet insurance records with both of us listed as owners. Secondary evidence, yes, did not hurt one bit to include. 
 
Good things to do. Probably the best things to do, really. Consider adding her to your auto insurance, renters/home insurance, and medical/dental insurance. 
 
People will say that affidavits are secondary evidence, and they are--and so are pictures. Include 2-3 affidavits, won't hurt. The affidavit from my husband's (USC) parents was one of the two things that the IO actually read during our interview. Doesn't hurt. 
 
Aim for 5-7 pieces of the same evidence max. No one will read hundreds of pages of text messages. Put yourself in their shoes, would you? Print a few, ranging in dates, if you want to include that. 
Try for a 2018 tax return filed jointly, assuming you were married in 2018. Add her to your utility bills, even if she doesn't financially contribute. Consider a family cell phone plan. Any joint memberships you have, library or Costco or museums, won't hurt. But the best proof is financial, so insurance, joint accounts, joint bills, joint taxes. 

People do add hundreds of photos to the application. I'm not saying it will hurt your case, I'm just saying--pretend you're an immigration officer. You have a case in front of you. You have 10-15 minutes to review it. Will you look at 500 photographs? Or will you look at the first 10 and file the rest away? There's no point to overdo it. It's kind of like quantity_variety >= quality_variety > quantity_all. Variety of proof is best, then the quality of that proof (joint accounts vs affidavit from a friend, for example), then the actual amount of each. 
 
This isn't immigration related at all, purely personal. We have two dogs, one adopted and one insured since she was 2 months old. When your vet tells you they should really operate and it'll cost you $3.5k, you'll be really glad to have insurance rather than consider if $3.5k is "worth it." The earlier you get insurance, the cheaper the premiums. Again, personal opinion only. 
 
Eh. You can always change it later (name itself, or just on the documents). I opted to keep my last name for this reason, but you can always call up your utilities company and tell them of the name change. I'd say USCIS proof is more important than X County Electric having the most updated name on file.
Yeah, it's a pain. You're correct for required proof. As mentioned, there are ways to expedite the EAD. Once the biometrics are completed, about a month after you submit the application, she can start applying for jobs. If she gets a job offer, she can request an expedite. Approval is not guaranteed, but you don't lose anything by asking. The requirement is a job offer and a letter explaining why not accepting it will be a financial loss. If you can't prove any financial loss at all, then it is unlikely to work. Depends largely on your financial situation as a family and the career field vs her education background. On the latter, I'm referring to "this is an excellent career opportunity for my field and not accepting it will be detrimental to my overall career growth."
 
In the meantime, add her to your home/renters insurance. Add her to your medical/dental insurance as well, unless it's financially silly. You do NOT need a current SSN to add a spouse to your health insurance, despite some companies insisting on it. Call. 
Post your cover letter for the package here. It should outline everything you're including for each form. People will be able to spot gaps if you have any, but at the very least, it'll force you to organize. Good luck!