Can wordpress meet my needs?

I need to build a website for a company, not my company, a client. He needs a simple informational web site. It doesn’t need shopping cart/checkout or anything complicated. The main purpose is to list products that they manufacture for customers to view. Afterwards their customers order via telephone/fax.
The business owner needs full access to update the site. Preferably he should have the ability to create additional users. The main function is to add products. There will be a side menu on every page of the site linking to a separate page for each product category (they have a lot of products). He wants to be able to edit the order of how the products appear within each category’s page (i.e. not necessarily should they be in order of newest-oldest or a-z). He also wants to have the ability to change the order of the product categories on the menu.
I also need to create a form for the “contact us” page and leave control to him of where they are sent to (in others words he can change the e-mail address). There should also be an efficient, working, and normal-looking product search engine for the page (not those cheap kinds that bring you to a new, different-looking site for the search results).
I am new to wordpress and my only experience with it is playing around on wordpress.com. However, I understand that the normal wordpress software which you install on your own hosting gives you much more control over the website? Please if anyone can answer if worpress can meet these needs, and if so how do I start. Do I need certain plugins? If yes, which and how do I install them. Thanks in advance.