How do I integrate accounting and logistics software into an all in one system?

I would be starting an online clothes shop. Instead of having 2 systems act independently when an order comes in where the logistics system would handle which item warehouse should be packing and the address to be sent to while the accounting system handles the bookkeeping of which item was purchased and also delivers the invoice to the customer as well as prints a copy for internal storage, I would like the 2 systems to be integrated so that all of these happens simultaneously and saves on unnecessary steps in between. Is there a way to do that?

A lot depends on what specific accounting functions you need to perform - most shopping carts (even the most basic including Paypal, for example) will handle the inventory, packing notes, creating customer accounts, recording payments and invoice creation with ease but accounting is more than just invoicing. Do you need to be able to enter costs like hosting, advertising, staff etc? Do you need access to budget reporting, P&L, balance sheet?

If you just need invoicing then any cart will do it for you - if you want the full blown accounts experience then you will need a cart which can integrate with accounting software. Magento, CS Cart, Opencart and more have accounting integrations though I have not used them and am simply relaying some of the options.

You need an ERP system for accounting, warehouse, invoicing, purchases even sales. You might want to use another CRM if you selected ERP doesn't have a good one. I suggest to look at OpenERP (www.openerp.com) it worked nicely for a few customers of mine.

Online shop such as Magento or Opencart are good choices for a frontend store solutions and those integrate with ERPs easily.