Yep, we received rotisserie chickens (and baked chickens too) after the birth of youngest son. I had a post-partum doula that came to help some, so I asked her to shred the chicken for me. Previous commenter asked about your oldest doing that (good idea).
From there, I could easily mix up enchiladas (I used canned soups and pre-grated cheese as I just wanted my family fed). I think we did a chicken rice and broccoli casserole too. Frozen broccoli or other frozen vegetables (or canned if that is your preference) work well for this. It's a pretty easy meal to throw in a pan or the crock pot.
As far as staying fresh, I think they are fine for 3-5 days or so.
(again) on your new blessing!