Urm.. tell your employer, supervisor, director or whoever is in charge of your department that website design doesn't just use 1 application. Although Photoshop can do the coding for you, it doesn't do all that you might want/need later.

Anyway, bear in mind that each of the programs listed above won't be able to do everything you'll need in Website Design. Here's a short breakdown for you and your supervisor if he/she cares to read it.

Adobe Photoshop
..is a bitmap graphic program which is half the time used in graphic editing like photos and nowadays, websites. Photoshop can export finish design for websites with ready made codes however the setback is that Photoshop will not allow you to implement dropdown menus or make form creation easier for you to do. This means that you'll have to use Notepad or someone who understands programming to accomplish the more demanding dynamic tasks later.

Adobe Illustrator
..is a vector graphic tool used normally in print. Sometimes its used to create Scalable Vector Graphics (SVG) to be exported and used in Flash. The biggest comparison of Photoshop and Illustrator is that Illustrator doesn't let you export into a HTML file with the coding done for you after slicing it. However, the biggest advantage Illustrator gives you is it allows you to scale your created graphics into various sizes without loss of quality unlike when done in Photoshop, it blurs if you try to blowup a smaller sized image.

Macromedia Fireworks
..is basically the Photoshop of Macromedia (now acquired by Adobe) and because of the recent merger with Adobe, the company might not improve or support this software in future. They just might merge what Fireworks have with GoLive or even Photoshop. So what you'll need to think about Fireworks is future expansion and will you need any unavailable support later for this application.

Others
..is basically asking for a tool that can do everything. In other words, you're asking an accountant be a CEO, CFO, designer, programmer, secretary and etc. Even if there is such a tool, I'd ban you from getting it because it won't fulfill all you'll need in the demand of website design today.

Hope all of that helps.

cheers.