The ones on my DreamHost hosted sites are easy and a dream- they have one click install/updates. I just click and wait a few minutes. I was wary at first, but there has not been a hitch in 2 years.

For the ones I do manually, I stick to the recommended steps. Some suggestions:

* WordPress Data Backup plugin makes it easy from your WP dashboard to run a backup, can have it saved to your wp-content directory or emailed (not a great idea with a 37 Mb db). It also can do it on a schedule basis (I think)
http://www.ilfilosofo.com/blog/wp-db-backup

* Maintenance Mode plugin - When you are updating you are missing/adding files and who knows what happens when people access your site? This puts up a splash “come back soon” page for visitors, but as an admin you can log in and do stuff / check. When you disable all plugins, just activate this one. When things are done, I de-activate this one.
http://sw-guide.de/wordpress/plugins/maintenance-mode/

* At first I thought 37 Mb was oversized for a WP database, but that within reason, especially as PodPress creates tables, and if you run Spam Karma 2 that creates big log tables, plus you have lots of long blog posts and comments Mine is about 20. I good habit to do maybe monthly is to go to phpMyAdmin for your database and click the little link below your tables “Check Tables Having Overhead” - overhead is wasted space, and this selects the ones with this (amounts listed in right most column) and then select “Optimize Table” from the menu to the right. This can clamp down a lot of space, plus will make your database run more happily.

* A simpler way to backup for update purposes is to do a copy in place of database and files rather than downloading (although I recommend downloading on occasion). In phpMyAdmin, got to your database, and under the “Operations” tab, look for the “Copy Database to” field and just give it a name like “wordpress.old” with the default options. This makes a copy right on your server. If something goes swry with an update in the database, you can delete your original, and then rename this copy back to its first name.

At the same time, downloading your entire WP directory can take a long time for file transfer. Actually, all you really need is the wp-content directory and your wp-config file (I keep the htaccess one too) as everything else is what you replace. An easier way during upgrade when you want just an “in case of disaster” copy, is to make a copy in place on the server. This means you have to be able to log in to your server on command line (telnet, terminal) and not all hosts allow that. If it does, you just need to navigate to the directory that contains your entire wordpress install, which may be a folder named “blog” or “wordpress” or even “jellybean” and then just do a unix cp command

cp -r blog blog.old

The “-r” tells it to copy all of the internal folders recursively so you get everything.

This way you have an emergency backup w/o needing to ftp down and back.

Lastly, I heard Matt Mullenweg say in a speech in February that on the roadmap is an ability to upgrade WP in place without this manual mumbo jumbo, the way plugins can be done in the 2.5 version. There is a plugin that sounds like it does it, tho I tried a while last night with one of my minor blogs and could not make it go:
http://techie-buzz.com/wordpress-plugins/wordpress-automatic-upgrade-12-release.html