Doesn't matter. There is no toothpaste that works better or worse with chlorhexidine.
Any but rinse well. If you use chlorhexidine, you should rinse your mouth well w/ water after brushing your teeth & before using chlorhexidine. This is b/c some ingredients in toothpaste can inactivate chlorhexidine. Chlorhexidine can also stain teeth brown when used regularly. This staining is likely to need to be removed by a dentist or dental hygienist.