I can only speak for the 1and1 half of this as my friend did the sql dump at Site5.
I updated the database name in the sql dump. I uploaded it using MySQL 5.0 (I previously used MySQL 4.0) and phpMyAdmin. I made my edits using BDV Notepad.
When I had the sql dump file open in BDV Notepad, some characters (em dashes, smart quotes, u with umlaut, etc.) looked corrupted. However, after I uploaded the file, they appeared fine.
My previous attempt to edit the sql dump file in MS Notepad seemed to corrupt many special characters. My attempt to upload the file after editing failed several times. I think this had something to do with the UTF character encoding. The solution seemed to be to change as little as possible. Though, I did cut out around 2mb of unnecessary rss info that I think was generated by something called Magpie RSS.
I had all the WordPress directory ready to go on the new server. So, I followed the directions here: http://codex.wordpress.org/Changing_The_Site_URL
4/20/2010 Update: I had to upgrade my MySQL version to upgrade WordPress (to v2.9.2) and found I had a really tough time working with the SQL dump. After several hours of searching, I finally came across this: SQLDumpSplitter. After installing this and splitting the file, the SQL import was simple.