I use an Astron SS-25M with my IC-718. You want at least a solid 20 amps capacity if you are going to use the full 100 watt output. Astron and Alinco make pretty good power supplies. Mine is a switcher, but with such great filtering that there is no detectable noise on the output.
I used to use a deep cycle RV battery and small charger or solar array, which also worked pretty well. I still use this for portable operations, like Field Day. I bought the IC-718 specifically for portable use, and it is a very capable rig.
Tuning the IC-718 for distortion-free AM is the same on any band. Select ALC as the meter function. Go to the "Mic Gain" and speak normally into the microphone. Adjust so that the ALC doesn't peak past the ALC zone, which is about 60% of the way up the meter. You can do this in AM mode. The "COMP" speech compressor does seem to keep the average power a bit higher, but I haven't seen it make as much difference in straight AM as in SSB. It doesn't help at all in FM.
That should give you a good starting point, and then you can tweak it in based onpreference and signal reports.
You might want to set the Squelch/RF Gain selction while you are in the menu to SQ (squelch only) or AT (auto). In auto it selects squelch only AM, Squelch/RF Gain for SSB.
Dave_W6DPS