What kind of website do you want to start up? If you intend to ask for a company website, then you could possibly include all the services which you are willing to offer. You should also probably include a contact form/request a quote form for visitors who may be willing to avail your services.
Where are you based? Normally the web design company takes care of the SEO it saves having to share your idea with two separate parties. It would be a good idea to share some information such as your area, your language, and your target sector, and possible how much you’re willing to spend. Alternatively you could learn yourself and do it for free.
There are a number of SEO companies that can offer you discounts on your SEO when taking out a website, I've PM'd you with some details.
i suggest that you should do your self every thing in starting, because no one can do much better as you can.
Choosing right seo firm..you need to check whether they are offering end to end Solution, since you want service for new site so, your site may be having some issues from Customer and Search Engine point of view.