The first logo, first used in 1993-1997. However, it first debuted on a rare VeggieTales promo from 1992. It can be seen here: https://www.youtube.com/watch?v=F5qKmOhjs8U. The last video to use this logo is the original print of Josh and the Big Wall (1997).
Same as the first one, but the text is yellow and a purple rectangle. It was premiered on Madame Blueberry (1998). Despite making an appearance on Abe and the Amazing Promise, the last video to use this logo is Abe and the Amazing Promise (2009).
Premiered on Minnesota Cuke and the Search for Noah's Umbrella (2009).