I used a diaper service for my daughter until she grew into her borhter's old medium diapers (about 5 months old).
I am really glad I chose a diaper service and here were my reasons:
You never know how big your baby is going to be when born, so it's so hard to know what size to buy. If you have a premie or a 12 pounder you know you are not waisting money on diapers that don't fit.
Babies grow SO FAST those first couple months, and with a diaper service you don't have to worry about buying the next size up every 2 weeks, or trying to get prefolds that clearly don't fit - to fit just a bit longer! I just called them up and requested a bigger size when ever she outgrew hers. In 5 months we went through about 3 sizes!
Life is so busy those first few months that ANYTHING that saves time is great, in my book! The diaper service we used picked up the diapers on Friday morning and delivered new ones at the same time. The ONLY work I had was putting the clean diapers away, and keeping clean ones on baby!
And, I washed my own covers (which, I rented).
My package was 80 diapers a week, with 6 covers rented. It worked great for us.
Now that my daughter is older, I like the flexibility of washing my own diapers - and that I can have some fun AIO's and fitteds too. It did get boring using white prefolds with a white cover for every changing. :LOL
Good luck and congrats!