For wire antennas the "A" answer is going to be a fan dipole. These are tricky to tune and not very fun to look at if you've got any WAF issues (wife acceptance factor), but you can't beat a resonant antenna for performance and you should not require a tuner for it either.
If you just want to put up one really big wire I'd suggest going a different route on your tuner. Instead of the LDG tuner, get an Icom
AH4. The AH4 is far more optimized for that sort of thing. If you can put the center of the dipole at the tower and put the AH4 at the top of the tower right at the center of the dipole then you will avoid the loss associated with a coaxial feed to a balun and also avoid the tricky use of ladder line. And the AH4 control/power wire will plug right into the back of the IC718 allowing the rig to control the tuner.
The AH4 is kind of pricey. An alternative to the AH4 is the
SG239. The 239 is not weatherproof, but it is a simple matter to put it inside of a weatherproof electrical box. The power for the 239 can come from the tuner port on the back of the 718, but you will not have the automation of the AH4/718 combination, i.e. you will have to key the 718 manually and let the 239 tune by itself. Not a big deal, that's how I run (Flex 3000 with SG239), but it bears mentioning.
Here's a pic of my SG-239 in a box. Also shown in there is an MFJ bias tee, which I used to run power instead of a control cable. I will be replacing it with a control cable, though, because I have a home-brew SGC "
Smartlock" controller that I want to use. Oh, and if you do go the big wire/tuner route, a few ferrites on your coax to act as an RF choke to prevent any currents coming back down the shield are very advisable.