Site search on a blog: The more content, the more posts and comments, the more you need site search. Especially if you do not have subject categories or tag clouds.
There are two types of site search: 1. Internal and 2. External
Internal: Some blog platform/CMS software had their own built in site search. These can be a mixed bag for relevent results, but they provide coverage right away.
External: Like a site search box from Google, Bing or some other search engine, can be better for some blogs, especially very popular blogs. But if your blog is just starting out, it might take awhile, even months, for the search engine’s spider to index every page on your blog. And then the search engine may not recrawl very often to index new posts. This will change gradually, time, popularity, link backs and frequency of posting, post length all factor into how frequently a search engine re-spiders a blog. So on a blog just starting out there may be gaps.
New blogs might want to go with the Internal search option early on and add the external search later. If your blog platform does not provide Internal site search then add an external search box straight off. Do your best for your readers.
Google still appears to provide free site search. Duckduckgo also has site search. Yandex also offers a free site search option.