Find out what the strengths and weaknesses are of your team. Some people might be better at graphics, others at coding, and some might be better at communication with clients etc. Use the strengths of your team.
A lot of steps! One of the first things you should do is find out the purpose of the web site. Consider the target audience. For example, you mentioned seniors will be using the site. That means you may wan to have large, simple text content and keep the site simple.
When you are doing the redesign, look at the old site and look at the way the content is structured, this may need to change according to the purpose of the site. Come up with a few design mock ups and brainstorm with your team to see which ones are best, and what you like about each of them.
Since it's a school/class project, you won't have much communication that often with the representatives. This is different in the real world experience (at least in my experience), you will be constantly having back and forth communications with the client, mostly to keep them up to date and to ask for input.
I'd divide up the content, coding and graphics between the 3 (or is it 4?) of you, depending on who's good at what. There's no sense in having 3 people updating code at once, even if you're working in separate pages, because that can cause problems. I've done this before when more than 1 person is editing the same file and one person's edits get overwritten. Make sure you're always communicating what you're doing.
But before you start any coding or touching any editing/design programs, make sure you have a plan of what needs to be done. That way, you have something to go back and reference, if you're unsure of say, what color a heading should be, or what should the text on a image say.
And finally, since it's a class, try to have fun and learn something. I remember my projects class, we didn't quite finish the site, but we learned about project management and working together as a team, which was the important part.
That's all I can think of for now.
EDIT: Forgot to mention testing. Never overlook this, or assume something will work, trust me!!