Speaking of designers, should I be looking to hire specific calculator designers or should a reasonable web design firm be able to handle this sort of thing?
Web designer is fine. In regards to the quality of the interface (calculator).. you get what you pay for. Some are better at designing for user experience than others.
What are the advantages/disadvantage to jQuery?
You can't compare PHP and jQuery as they do two completely different things.
jQuery is a JavaScript library - it has many benefits, but mainly it just simplifies the JavaScript language. One of the main benefits is that it eradicates most cross-browser inconsistencies that JavaScript has. JavaScript does all it's processing in the users browser (client side). It's predominantly used to pretty up web pages (show/hide elements, animate etc).
PHP works on the server side. Among other things, it's used to write and write to a database. It can also send email.
Having said that, you can use PHP and jQuery together via AJAX. AJAX allows you to do things like read/write to a database without reloading the entire page.
So if you want a web form (calculator) that dynamically pulls information from a database based on the users input/selections (the variables you mentioned), then the best way IMO is to use a combination of PHP, jQuery and AJAX.
I hope that makes sense!
Prices and availability for the products will vary from area to area based on suppliers, so I will also need to enter in the supplier's details and product pricing (will this mean I need a database or something)?
You can do it without a database, but I wouldn't recommend it as it would be a nightmare to maintain.
Like Tim said, outline the process set by step and then use it to get quotes.