Its probably best to look for a mobile friendly theme as not all are and mobile is where a fair percentage of your visitors would visit via... as regards to SEO which ever theme you decide to go with you can add an SEO plugin which will help you with SEO ing your pages and posts I would recommend SEO Yoast plugin for this... trust this helps

Thank you mcb247, I am definitelly going to check mobile compatibility and all technical acpects etc., I know what to check in general, I was a Wordpress developer myself back in the day So I know all about it - I just never cared about SEO at all and never optimised my themes like that hence my quesion, I'm sure some are better than others in that area.

Most modern themes are seo friendly, and they also mention this in the theme specs. Anyone of those should be good.

However do ensure that the theme is mobile friendly.
I use the free Hueman theme - https://wordpress.org/themes/hueman/

Here is a collection of responsive and SEO ready Wordpress themes that you can apply for free:

1. Swift Basic – Free WordPress Theme Responsive

2. Business – Free Responsive WordPress Theme

3. Constellation – Free Responsive WordPress Theme

4.Zenon Lite – SEO optimized Responsive WordPress Theme

5. Gadgetpoint – Free Responsive WordPress Theme

6. Caja – Free WordPress Theme

7. Libra – Corporate & Portfolio WP theme

8. Sensitive – Responsive WordPress Theme

9. Pytheas – Free Responsive WordPress Theme

10. Skeleton – Responsive WP Theme

It gets better with the Wordpress SEO by Seo All in One -

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