Help with WordPress Organisation

I am currently setting up a website for a client and have come across a total mind blank, the site is a brochure website but has a section of products from a product catalogue. The products can be broken down into categories, example below.

• Products (main category)
• Manual Wheelchairs (sub category)
• Wheelchair 1
• Wheelchair 2
• Wheelchair 3
• Mobility Scooters (sub category)
• Mobility Scooter 1
• Mobility Scooter 2
• Mobility Scooter 3
• Walking Aids (sub category)
• Walking Aid 1
• Walking Aid 2
• Walking Aid 3

Etc etc etc.

But I just can't seem to work out how to organise this, maybe I am over thinking it, but a custom post type of 'Products' was my first thought and have each product created be assigned to a category (Manual Wheelchairs, Mobility Scooters etc) and then display the products assigned to each category when clicked, but for the life of me I cannot get this to work ... What template should I be using to display the products? Should it be a custom post type? Do I use WP_Query to display the products? If so how do I display the products in each category without creating a new template for each category?

Apologies for all the questions but as I said my mind has just went blank ...

Any advise anyone can offer would be much appreciated.

Thanks.