It is good to wipe your guitar down after use and yes an occasionally a polish is in order, I always use polish extremely sparingly, you actually get a better buff when you use a little. Some of my 20 year old guitars still look new from regular maintenance. Even guitars left in cases have to be checked and maintained. I try to only have as many as I can maintain, that's about 10 or 12. If I had more than this I would spend my days maintaining and not playing.
Playing a well serviced guitar is the way to go and your guitar sounds better.
I always wipe the strings before and after use as I hate corroded strings.
Some products I use are the Rickenbacker cloth that came with the guitar and a Dunlop finishing cloth. I use a product called Zymol to polish my guitars it's expensive as gold but one jar should last a decade or so if you keep it in the fridge ( but not in children's reach). I love the smell of that stuff! Zymol gets used extremely sparingly as it's rich (but doesn't go gluggy)
I have a question for you. If I remember correctly you own a 350v63 as well as this 360. Do you find the 360 easier to play than the 350v63. The 360 has neck binding the 350v63 doesn't. Does the 360 seem to be easier for your Left hand technique as far as your playing foot-print is concerned?