What Shipping extension do I need?

I have a store which requires the following type of shipping charges set-up for orders:

1. Baseballs are charged at £10 for first item and £5 for each subsequent item for UK orders only
2. For European orders I then have 3 different zones where the shipping price is different for each zone, so, for example, zone 1 baseballs are charged at £20 for the first item and £10 for each subsequent item and so on.
3. Boats are charged as free shipping for UK and all other zones

I need to be able to set up the shipping to reflect these different shipping areas and be able to include the free shipping. So what I need is a set up which will do this:

ORDER FROM THE UK (but this will apply to the other zones as well, I just used UK as the example)
1 x Baseball = £10
2 x Baseball = £15 (i.e. £10 for the first and £5 for the second)
3 x Baseball = £20 (i.e. £10 for the first and £5 for the second and £5 for the third) and so on

The other scenario is a paid shipping plus a free shipping:
1 x Baseball and 1 x Boat = £10 (i.e. £10 for the baseball and free shipping for the Boat)

I was thinking that the Product based shipping extension from Get Clear Thinking http://www.getclearthinking.com/shippin ... d-shipping may be appropriate but I'm not 100% sure it will do the job?

Yes, Product-Based Shipping will work for this setup. You'll need to set up rates like so:

RATE #1
Sort Order: 1
Multi Rate Calculation: Sum
Geo Zone: UK
From: 0, To: 999999, Charge: 5.00, Per (#): 1
Final Cost Min: 10.00
Product Criteria: ANY
Products: (baseballs)

RATE #2
Sort Order: 1
Multi Rate Calculation: Sum
Geo Zone: (all geo zones)
From: 0, To: 999999, Charge: 0
Product Criteria: ANY
Products: (boats)

RATE #3
Sort Order: 1
Multi Rate Calculation: Sum
Geo Zone: Europe
From: 0, To: 999999, Charge: 10.00, Per (#): 1
Final Cost Min: 20.00
Product Criteria: ANY
Products: (baseballs)

That seems perfect for what we want. Sorry for the late reply. One last question...do you know if this extension would be compatible with Opencart version 1.5.3.1?

Thank you again.

Yes, it should be compatible. I just haven't marked all my extensions as such yet.

We are starting a multi vendor online shop and installed the VQMod extension to manage this. We need each vendor to setup their own shipping rates within each product or by way of weight based shipping if multiple items are bought from a single vendor and as the main store be able to add the vendor's courier companies as options which they can use for shipping. What is the best extension for us to use?

ie Vendor A sells Product A+B shipping on A is R100 and on B is R120. If they are bought together, the weight based shipping should be used to determine a better rate for the buyer ie R180 for both products. If they are bought separately, the per item shipping should be used.
If a customer purchases from more than one vendor at a time, the system should calculate each vendors shipping separately.

Please advise!

Because you're using a modified installation, it's unlikely any shipping extension will work for you. I recommend you post a request in the OpenCart "Commercial Support" forum, which is checked by a number of OpenCart developers.