Does the site already exist on Wordpress?
So there is no need for a new installation, you can just create a new website / blog and call the posts. Why could not he stylize? Of course you should marry the rest of the site, but you can style what you want on a single page through css.
Anyway, there is no problem also if you prefer to do a new installation in subfolder. I just find it unnecessary for a new configuration and hosting space.
There is no rule regarding the folder or subdomain blog.site
If you prefer subdomain you can choose a new installation as well or use the multisite function that may make your life easier, since you would have access to the same settings and at the same time would give you the freedom to use an independent theme and other functions.
At the SEO level it would be slightly better to use the blog in paste instead of subdomain because it facilitates linkjuice logic.