Influence of blog theme on SEO?

Hi guys

I'll be launching my blog about one of my hobbies soon. I've chosen the WPZoom Magazinum theme because it has a good balance between text and pictures and I also like the minimalistic look. One specific site (sorry, can't link), however, says the theme is quite bad for SEO. Is this true? I thought themes had little influence on SEO? Can I improve this using a good plug-in (e.g. Yoast's)?

I'm also wondering if it is better to build the blog offline first and then upload it or put it online immediately and then work on it. What is better?

Pictures will also play an important role on my blog. Do I need to take this into account when searching for a good hosting service or will 3000mb be sufficient?

Thanks for your help,
GiFr