Your trip will be very easy:
Take I-70 from Denver out east to Salina, Kansas and get on I-135 south through Wichita where you will join up with I-35 south. Stay on I-35 through Oklahoma and into north Texas where you will get into I-35E towards Dallas. Don't go through central Dallas (unless you like driving by skylines) - take I-635 around town and get onto I-20 eastbound to Shreveport, Louisiana where you will merge onto I-49 south into Lafayette. Then in Lafayette get onto I-10 eastbound right into New Orleans. After your stop in New Orleans, stay on I-10 until you get to the I-75 junction in Florida and get on I-75 south right into Naples.
These directions will tell you to go some weird way around Lafayette, but you will want to stay on the interstates.