I also have a newly acquired P800, but it was preceded by an Epson 3800 (seven years) and an Epson 2200 (five-ish years?) before that. My 3800 was incredibly reliable with very little maintenance. My home has whole-house air conditioning, humidification, and dehumidification, so the humidity level in my home office never gets below 30% or above 50%. I believe that has helped.
In addition, based on my own experience and what I've read on the web from others, my own recommendations are as follows:
1. Control the humidity level if you can.
2. If your location is dusty, keeping a dust cover on it when it is not in use could be helpful (I seldom bother).
3. Opinions seems to be divided on whether to turn the beast off when you aren't using it. I generally turned my 3800 off when I knew I was going to be away for a few weeks, but not otherwise. I'm doing pretty much the same on my P800.
4. It is good to do a nozzle check at least once a month, and then a nozzle cleaning only if the check shows gaps. I almost never bothered with nozzle checks on my 3800, but about once a year I wasted some paper making prints that looked awful. At that point I would do a nozzle check, which showed me why the prints were bad. And I then cleaned. Only twice over seven years did I have to do multiple cleanings. If two cleanings don't clear the nozzles, leave the printer overnight and try again. Another nozzle check and cleaning at that point will almost always clear things up.
5. The only times my 3800 gave me problems with paper feed were when I had run a bunch of double-sided sheets through the printer. Even if I let side one dry over night, the ink on side one would get onto the rollers when printing side two and eventually make them lose traction. On the few occasions that this happened, I sprayed some Windex glass cleaner on the middle of a sheet of cheap matte paper (which I no longer use for prints) and ran it through the printer, followed by two dry sheets. That always restored the print feeding with nothing else needed. I plan to do the same on my P800 if it ever needs it.
6. It is probably good to make a print or two almost every week, but I have left my 3800 for as much as 6 weeks untouched with no ill effects. I doubt if the P800 needs to be babied very much, given its similarity to the 3800 and 3880, which have been spectacularly reliable (especially compared with some of the larger Epsons).
7. Enjoy it, and make good prints!
Good luck. I hope this helps.