and welcome to this site. :-)
You should not use
http://company.blogger.com -- it looks unprofessional.
If it's possible, then the classic advice is to keep as much content as possible on just one domain name, i.e. www.company.com/blog/ .(company.com is one domain name, www.company.com is another, and blog.company.com would be another domain again.) The reason is that search engines calculate 'authority' (Pagerank etc) based on inbound links, and inbound links are counted on a per domain basis. Thus having multiple domains leads to your 'authority' being diluted/reduced.
However, there is another argument to consider. www.company.com must point to a specific set of IP addresses, i.e. specific servers. Sometimes it can be very advantageous for operations to use another name like blog.company.com , and let it point to a completely different IP address -- f.x. keep "www." on a hosting provider who is good at general hosting, and keep "blog." on another provider who specializes in blog hosting.
As I understand this interview with Matt Cutts (~8 minutes in), the differences in sub-folders versus sub-domains has been diminished in Google's rankings. Maybe other (older) search engines still care a lot, but Google does not see the difference as large as they used to.
Thus you should select either
based on a reasoned assessment of SEO properties, and what is more manageable for your day to day operation of your website infrastructure. In general, www.company.com/blog/ is "best", but only if it doesn't require large effort to set up.
Another thing is you should not move your current blog URL without good reason, a good effort into providing redirects for all published blog pages.
Another question is to "www." or not. Here is one fair opinion -- above all, just be consistent.