I should add, finding a 22LR firearm is likely something you'll use for years to come. Nothing comes close to 22LR in cost, although it usually pays to not buy the cheapest 22LR.
A couple of notes, since you sound new to this:
-22LR is a rimfire, and the cases are not reusable. The centerfire ones are reusable (usually), and reloading your own ammunition is a great way to control costs--but it's doubtful that you could approach the cost of 22lr, even with reloading.
-Remington 22lr is usually lousy; I'd avoid. Very few people have been happy with it. At least going off what the internet opinion is. Yet Remington still sells lots of it, so...?
-I like CCI Mini-Mags, they work great in pistols. You shouldn't need anything exotic like Eley, or "have to" use standard velocity, or the like. My Ruger likes Federal Automatch, which used to be available at a good price at Walmart. A hundred rounds of Mini-Mags is usually $6-7, give or take. Fed Automatch was like $14 or so for 325 rounds.
-22LR is notoriously dirty. So far my Ruger's don't mind the dirt. Some pistols are notorious for jamming up after x rounds. Not saying you should not clean after a range session, but it's nice when you don't have to clean *during* a range session. I doubt that the M&P would be picky, but I've never read up on it. Some of the other 22lr's certainly can be.
-rimfirecentral.com is a good resource. There are probably other good sites too out there.
-buy ammo as you see it. Who knows when it'll be in stock again.
-Despite being "just a 22" you still need ear protection. Regular old earplugs will work fine, or whatever you might use. Don't need much, but a 22 pistol is still louder than any 22 rifle that you may have used in the past. If you shoot at an indoor range, or in particular around others, get good protection--as others may be using large(r) caliber firearms, which most likely will be much louder. Eye protection should be worn too, although like others I usually just wear my regular prescription glasses.
-Does the M&P have a rail on it? I doubt you'd ever scope it, but a red dot can be fun. I'm looking forward to setting up a red dot on one of my 22's some day. Iron sight shooting is fun; it takes practice. Red dot's can make it easier, and make shooting faster, which is fun itself. You might not want a red dot today but you might want to try out some day. Also, it can't hurt the resale value either.
-take a look at magazine cost. Not saying you want a hundred mags or anything; but it can be nice to reload a bunch ahead of time. But if the mags are $50 apiece that might be intolerable, even for just a spare magazine. [Magazines don't last forever. Some do, some don't. Nothing lasts forever, so having a spare in anticipation isn't a bad thing--nothing like ruining a day at the range when you find a mag that won't run. And often they just need a good cleaning, so it's not necessarily a wear thing.]
-Figure out where you plan to shoot. A membership to a range might be good. A number of the regulars love to let others try out their "toys".
-Do you plan to shoot indoors? There are some lead exposure issues you should be aware of that you wouldn't run into with outdoor shooting. If you shoot indoors, make sure they have a good air filtration system, that they don't use brooms on the floor, etc. [Most primers used in ammunition contain lead, which gets into the air, and will also settle onto the floor. An indoor range should use a shovel to scoop up brass, so as to not kick up lead dust.]
-22's are often unplated bullets, but even on the copper washed ones practice good lead safety: wash your hands after handling ammunition and/or guns and after shooting, in cold water. You can't absorb lead through your skin, but through transference it can still get into your blood stream.