shipping system based on weight, size - I need help understanding process....

Hi all, ok I am having problems looking into the logic of setting up the follow shipping system.

The types of products are furniture.

So, items could be a small candle, bedside lamp, chair, table, bed etc. So varying weights and sizes.
Because of the product range the client is using 3 different shipping companies.
Royal Mail (for small items)
Parcel Force (for small to medium items)
PalletWays (for large items)

Each of the above have their own weights, sizes and delivery options and different tiers.

Now all this can be quite complex. So I am am working it out with the client so that we try and simplify it in some way, I need you guys help here.

on the basket page we will just have one delivery option (standard delivery) then the system will work out total weight of basket and calculate the totals for height, width and depth. taking these calculations it will then cross reference with what is stored in the system to calculate the cost. I think this system would work fine if it was single items in the basket, but because the basket can consist of varying sized/weight items and quantities of those, this is where my head is hurting trying to work out a system I can code.

I have already created admin pages where the client can create shipping costs, by entering the following data:
shipping option
shipping max weight (kg)
size (small, medium or large - (royal mail, parcel force or palletways).
shipping cost

I think thats all I need.

in the products table I am storing product height, width and depth separately and product weight.

Would it be easier for me to also create another field in the products table to categorize the product as either small, medium or large, that way I am force a certain calculation?

I am worried how I would work out the calculations? especially working out multiple products in basket, for example in the same basket, a customer orders a large bed which would need to be delivered by PalletWay as its a large bulky item, and in same basket, maybe 2 lamps with is more bulky to be classed as a small package for royal mail but small enough to be classed as a medium package for parcel force. These are my concerns?

It doesn't matter for the customer to know how many delivery companies will be used, I just need to calculate the shipping charge and then the client will determine the best delivery companies to use.

Can anyone give me any feedback, insights or tips please?

I need to most simple of solutions since I need to code it all in.

I need to get this done asap. thanks for reading.

Chris