I think you might just want to go for a theme with a page builder. The homepage sections (or services) are each a row with a background image, a heading, a text box and a button. Then you can build separate pages for each service,. Where your pages lead to is entirely up to you - you can just insert a button or callout at the end of each service page that leads to your contact form.
We’re of course partial to our Total WordPress theme:
But you really can’t go wrong with any of the top selling WordPress themes on Envato since most include page builders: