With my first, she exclusively breastfed for 8 weeks. I was never able to really pump either; and when I back to work, stepping away to pump was out of the question. With my second, he only breastfed for 10 days before I switched him to formula. I was dealing with PPD and a mild addiction to pain meds (he was a c-section). I still feel a bit guilty for not trying to pump, but he's a healthy, active 3 y/o now. And now I have an 8 week old that I'm pumping milk for and supplementing with formula. I'm able to pump as much I would like, but every little bit helps. He had problems with the letdown when my milk came in...pulled away choking, gasping for air. His doctor recommended pumping, but encouraging him to nurse. Now he won't even let me put on my breast.
My advice is to pump as much as possible between feedings. Continue to offer your breast because once they start on a bottle, they won't want the breast. For baby, getting milk from a bottle is easier and less work than the breast. At that age, it's easy to cause nipple confusion.
For breastmilk storage, I like to use the bags from Lansinoh. They come pre-sterilized and are double sealed. You can store breastmilk:
At room temperature: 4-6 hours, ideal being 4 hours.
In the fridge: 3-8 days, ideal being 3 days.
In the freezer: 3-6 months, ideal being 3 months.
In the deep freeze: 6-12 months.
The best way to thaw breastmilk stored in the freezer is in the fridge, which will keep in the fridge for 24 hours. But do not refreeze it.
Good luck and congrats on your baby!