Personally, I do this for every site I built unless there is some reason not to.

To start:

1. Build the website for a mobile display (not any particular one)
2. Once done and looking decent, add media queries to your stylesheet to make the site continue to look good as the screen width increases.
3. Once done, come back and use javascript and/or ajax where it makes sense to do so.

Personally, I'd recommend reading a good book on responsive web design. Some of the best I've seen are published by O'Reilly.

The easiest way is to use mobile friendly template.

Themeforest is the best place when you can find premium templates. If you want to use free template just google "free mobile friendly WordPress templates"

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1. Hard way- master your html/css/js skills and work hard.
2. Easy way- buy responsive theme(WP and bootstrap)

You can either use Media queries or Bootstrap to create responsive sites.I prefer Bootstrap....

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Easy way.. Buy a responsive template
Medium skills required... BootStrap
Skilled... CSS HTML Media Queries

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You can see this post on slideshare ,they shared lot's of important responsive tips there...
Responsive web design key tips and approaches

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