I’m going to base this reply off the site at https://www.storquest.com/ that you’ve linked in your original post.
All I see on that site is a theme, some contact forms, and a store locator. It isn’t very complicated. About 1 or 2 weeks for design, then 2 or 3 weeks for coding, plus 1 week for QA/bug fixes, it’s possible to finish something like that in around 4 to 6 weeks.
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Theme
The theme should be custom coded. You can base it off Underscores Starter Theme (it’s pretty much the official starter theme for WordPress) or Genesis Framework (if you’re into dealing with child themes).
Don’t use a pre-made theme. Only when dealing with low-budget projects (around $1000 or $2000 USDs) should we resort to a pre-made themes; they’re bad news in general.
Since you’ve never mention the budget in your original post, I’ll assume that the client has adequate budget–around $10000 to $15000 USDs. That’s enough to build a custom theme for the client.
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Plugin
Store locator plugin — If you Google/Bing search for “WordPress store locator plugin” (without the quotes), I’m sure you’ll find many plugins to use.
Advanced Custom Field (Free or Pro) — Your client will need to edit the content of the site without your help. And this makes it easy for you to implement custom fields for those content.
Contact Form 7 (free option) or Gravity Form (paid option) — That example site has many contact forms. Anyone of these would satisfy that need.
Also, Redux Framework is an option if you wish to give your client some control over the theme, but I generally dislike allowing the client too much control over the theme. They’ll ruin it. Better to not allow them those customization in the first place.
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That’s pretty much it.