Take a look at www.radioworks.com
for some nice antennas and a lot of helpful information. Their G5RV is here: http://www.radioworks.com/PDFCat2002/55.pdf
. Their Carolina Windom is also very popular.
Your internal antenna tuner in the Kenwood may not be able to satisfactorily tune the G5RV (or any other multi-band wire antenna) on all the bands you want to use. Most internal antenna tuners have a limited range and are primarily designed to "tweak" an antenna that is already resonant for a particular band.
I'm sure you'll get a lot of suggestions and responses on this helpful forum. Good Luck.