Company system building advice

Hi

I currently run an online retail business and the web site and system was built by me and to be honest although it looks good, and works to an extent, we are looking to get a company in to build us a full system for our company.

I am currently putting together a brief on what we need and want but I can make my mind up on one point:

We want the system to control all the workings of the business not just the web site, so stock control, suppliers details, invoicing, accounts, plus the web site end, with all the usual stuff and a few others.

But would it be best to be 100% web based, or would it be better to have a back office system that sites on the office computer system and have the web site seperate but linked, I am not sure how they would both link as i have never built a system this complex but my theory is if the internet connect ever goes down, no work will be able to be done, we as if there was an office system then in theory important work such as accounting etc will still be able to function as normal.

If you could let me know your thoughts on this, what the the pro's and cons of each and have you had any experience with them it would be appriciated.

Also what are the cost implications I suspect the 100% web site one will be less expensive but is this right, and who would I need to contact if I wanted the system which has an office based system and a web site based system, as i presume I wouldn't be looking at a web site company?

I Look forward to your thoughts and thanks in advance