An example: If my keyword is "dog training", it helps more ranking an url like: www. abc . com/dog-training or like? www. mysite. com Both optimized for "dog training"
If you are targeting so many keywords with your site then the keyword density of a particular keyword on the home page will be logically lesser then the main internal page. So its better that you target the internal page.
You can have sub-domains of keywords like "dog-training.mysite.com" and host pages in it. This will help in optimizing your site in more SEO manner.
It seems easier to optimize each page of your site for different keywords than to optimize your home page for all keywords. Consequently, I would say that a page optimized for one keyword would be better. It is actually something that I have had to do.