I like to use Hoppes #9 on my stainless guns, but refrain from use on my M&P340. Others have said they use it in moderation, w/ no problems.
On stainless, & blued guns, I also like to use spray solvents - but avoid them LIKE THE PLAGUE, on coated guns...
To clean copper fouling from the bore, I use BoreTech, & follow up w/ BreakFree CLP. Also use the BF CLP to remove powder fouling on the coated surfaces, & cylinder chambers. Applied w/ a blue paper shop towel, w/ a bit of light scrubbing - from a well worn, soft tooth brush. Seems to work out OK, w/ no issues to date.
The coating on the M&P340 (IonBond??), seems quite durable - to date.
Unless the action seems dry, or rough, I'd suggest a bunch of dry firing (I use snap caps), maybe 200 - 300+, before worrying about dis-assembly for internal lubrication. My D/A break was pretty heavy initially, but has improved substantially, w/ use.
After some prerequisite dry firing (& maybe a couple of range sessions), I always remove the side cover, hammer, rebound slide, & trigger - on newly acquired revolvers, for an initial cleaning & lubrication. When re-installing the internal parts, I usually use a few drops of Mobile 1, but BF CLP, or RemOil will work fine also.
For the record, I ordered a Brownells reduced power spring kit (Wolff springs), but only replaced the rebound spring. The main spring in the kit seemed to match the factory MS in weight, so I left it alone - for reliability.
The extended firing, the C&L, & the replacement RB spring, all went a long way towards smoothing up the action.
Enjoy your new pistola, I wouldn't want to do without mine!