You have the right idea with internal linking just don't over optimize the anchor text from your blog to your site.
As for content ideas your moving tips is a good start. I would also focus on getting customer reviews to help your local seo. Get either google places, trustpilot, or yelp reviews.
Other ideas could be moving nightmares to avoid, average cost of a move, moving scams, how to pack for a move, etc. The more creative you get the better results you will have. I highly recommend doing at least one info graphic per month.