Access to MySQL
First I have a very good overview article for you:
http://dev.mysql.com/tech-resources/articles/migrating-from-microsoft.html
I've recreated the data structure in my SQL DB manually, now I can export the data from Access as a CSV textfile.
You can specify which delimiters and quotes Access uses to export the data. Access escapes characters by using them twice, i.e. the string
I am a "very" skilled developer
becomes
"I am a ""very"" skilled developer"
If you want to import that PHPMyAdmin, you should process the file first with a text editor and replace all double quotes ("") by escaped quotes (\").