When I started blogging I used Blogger . After some time I decided that it did not offer me the freedom I desired. I could not easily make changes (I could have created new themes, but it would have taken an unreasonable amount of work). I currently use WordPress, it’s still a lot of work to change themes, but at least it’s CSS and PHP coding which can be used for other things. Blogger offers no statistics on web use (I tried adding support for Google Analytics but couldn’t get it to work properly), what I want is Webalizer or something similar (which is easy to do when running your own server).
Blogger is a reasonable way of starting blogging, but if you use it then you want to make it easy to change to something that you own. Blogger has a feature of using a DNS name in a domain that you own for the name of your blog (which is much less obvious than it once was), I regret not using that feature as I still have my old posts on blogger and don’t want to break the links.
Blogger has in the past had problems with time-stamps on posts, when I used blogger I had some complaints that my posts were staying at the top of Planet listings for unreasonable amounts of time (I never tracked this down before switching to my own platform).
Hosting your own blog is not as difficult as you might expect (initially at least). It becomes difficult when you want to install lots of plug-ins, but then any blogging solution would be difficult if you want to do that. The WordPress  package in Debian works well and has good support for multiple WordPress blogs. There is a separate product named WordPress-MU  which is designed for people who want to run a service in competition with Blogger, some people recommend that you use WordPress-MU if you want to set up blogs for several people. I disagree. If you are setting up blogs for a small number of people then you can use the standard WordPress package and create a file named /etc/wordpress/config-whatever.example.com.php which contains the configuration for whatever.example.com and then create a new WordPress blog by using the web-based interface to do the rest. It would not be difficult to create the configuration file in question with an M4 script if you have a moderate number of blogs to host (maybe a hundred or so). I think that it’s only if you want to host thousands of blogs that you need the features of WordPress-MU. Note that MU is not as well packaged as the base WordPress and has some rough edges. Last time I tried to set up MU I was not successful.
This is not to say that WordPress is inherently the best program, there are many other free software blogging platforms out there. WordPress is the one that I use and am happy to recommend but if your requirements differ from mine then another platform may be better for you. I also suggest that WordPress be used as the base-line for comparing blogging software.
Blogger does not require significant resources. A virtual host with 256M of RAM should be more than adequate to run WordPress plus MySQL. Such virtual hosts are getting quite cheap nowadays, and one such host could easily be shared by a number of bloggers. My blog uses about 1.2G of data transfer per month. vpsland.com offers virtual hosts starting at 150G per month data transfer with 192M of RAM being the minimum. Prices start at $US15 per month. While I can’t compare vpsland.com to other virtual hosting providers (having never used any other such service) I can say that they work reasonably well and I have a client who is happy with them. So it seems that a minimal plan with vpsland.com would host 20 blogs with the same traffic as mine (with RAM being the limiting factor) and a slightly larger plan (with more RAM and more bandwidth) that costs $US30 or $US40 per month could handle 100 or more blogs that are similar to mine. If you get together with some friends and share a virtual server then blogging would not be expensive. Incidentally I had previously read a blog comment about people being hesitant to share servers with their friends (as they apparently would rather grant some unknown people at a faceless corporation the ability to snoop on them than people that they know). The advantage of a blog server in this regard is that everything is public anyway!
If you have good technical skills then I recommend using WordPress as your first blogging platform. If you find that you don’t like it for some reason then you can convert to another platform if you own the domain. If you are setting up a blog for a less technical user then WordPress is also a good choice. My sister uses WordPress, not that she made much of a choice (I had set up a Blogger account for her some time ago which she never used – I guess that could be considered as a choice to not use Blogger) but that I set up a WordPress blog for her and she seemed to like using it.