I have a blog I am running for a small medical practice website. I want to know if there is any SEO benefit from putting the blog right on the homepage below a few paragraphs of static website content. I want the hompage to rank well, not the individual blog pages nor the blog page, so when google crawls the homepage, wouldn't it be better to have the fresh content right on the homepage? Or will google see that you have a blog somewhere on the website and then give the juice to your homepage? Or is it enough to just have the titles of blog posts show up in the sidebar of the homepage?
Yes, yo can list your blog post on home page and it works good, you can still optimize your home page with your targeted keyword, as you would be putting your targeted keyword in site title which is for home page.
I'd say it's a good idea because the blog pumps in fresh content to your otherwise (I'm assuming) static homepage. The content recency will help to make the page appear like it's getting updated more regularly, which appears to be a trigger for Google.
Its good to have your blog page on the homepage as long as it serves the purpose of your site. If you are a company which provides some kind of services It would be better to have a blog as a separate section and to talk about your business with clear call for actions on the homepage. Usability and little bit of common sense is what matters. If you are running just a blog site then its recommended to have links to your blog with a snippet of text on the homepage.