Alright. Here's what I'd instantly go in and check for (in no particular order)
1. Clean code
2. Great meta tags and meta descriptions
3. Descriptive H1 tag
4. Keyword density (make sure they're not over saturating their page, use different variations of words)
5. Hidden text, if there's any of that, get it out.
6. Link colour - make sure the links are quite clearly distinguishable in colour to the body text.
7. Make sure they're linking out to relevant authority links (news websites etc)
8. Don't over optimise it. Things need to be written for the customer/website audience, not for search engines.
There are tons of things, I could go on forever. Have a read of my
SEO Tips article.
The things they're going to want to know from you with an SEO strategy are things like;
- Where can we improve our site to create more custom?
- What is our return on investment? (If we pay you £4000, how much are you going to make us?)
- How can we maintain the traffic and customer flow AFTER you're done with the job?
SEO is changing lately, some say the term is dead. What you want to get them to focus on is content marketing. Get them creating regular posts and great landing pages that speak to and target their desired audience. The search engines are getting used to SEO and are looking for ways to deliver the best results to the end user at all times.
Seriously though, if you don't know how to prepare an analysis of a client's site, I'd consider handing it off. When people invest big, they expect big return.