For relabeling, the printers that I've worked with will remove the original t-shirt labels and replace them with custom screen printed labels in the neckline of the shirts. It isn't too expensive, but tends to add a lot of value to the brand. I prefer printed labels over sewn-in labels because they don't scratch the neck and are much more comfy.
For packing and shipping, you are best off ordering the supplies and handling the operation yourself. Check out my beginners guide to
product presentation and packaging. It should send you in the right direction.
Loren