If your lawn is almost ALL crabgrass then glyphosate or roundup is indicated. This is absorbed by the foliage and taken down into the roots where the KILL happens. Takes at least 3 weeks. Perhaps a second application. Read that label 5 times I kid you NOT. That is what they taught us as Pesticide Applicators. Five times!!
Do not spray in any wind, preferable to do in the evening when bees and birds and people are not around, regardless of the MSDS or label instructions. Before application DO NOT MOW. Do not use any other herbicide. The more vigorous the growth the better glyphosate works. Wait until all growth is brown, yellow, black dead.
If you don't wait 3 weeks minimum then any seed you apply will have trouble germinating. Don't worry about aeration, now is not the time. That is for an annual maintenance later once per year!
Then look up the lawn maintenance stuff on this site, quite a bit of it for you to learn and know so this doesn't happen again. Such as mow no shorter than 3 inches! Water deeply allow to dry and do not water again until footprints stay down on your grass. Fertilize 3-4X per year with season appropriate formulations. Again mow no shorter than 3"...ever. Otherwise, you won't ever see me giving others prescriptions for pesticides/herbicides! This is a major bandaid on a preventable problem but works well. Nothing else in my experience will work. Certainly not hand pulling, power rake for thatch...this will just leave roots and crab grass will definitely be able to come back if you are going to use seed. Make sure you grade, roll, rake again, roll before seeding. If you are going to use seeding I'd recommend hiring a grass seeding company to spray the seed and mulch and fertilizer at the same time. Otherwise, consider sod especially in your situation.