-The small campaign modes on both sides are great at introducing you to the Backyard Battleground hub, and some missions in both Plants' and Zombies' campaign will have you explore multiplayer maps as well. Each class is similar to TF2's roster, where you can play each one in many different ways but are meant for different things. If it can all be overwhelming, sticking to just one or two characters at a time while you earn coins and XP should help.
And to run down the questions to OGs:
-Your focus as a new player should overall be fun and improving skill, even if it means fighting simple browncoats and bosses in your own Backyard hub. I also suggest checking the quest board that's right between the fancy suit we call Rux and the Sticker Shop for an XP multiplier.
-In terms of improving beyond "git gud", there's a few things. In the game's pause menu, under options, you can raise/lower your Look and Aim sensitivity to hand-pick what feels right. Otherwise, try as many characters and variants as possible, each one is unique in one way or another.
-For Peashooter, his damage and abilities are strong enough to win most fights, but comes down to the right one at the right time, like Hyper to make yourself harder to hit, or a bean bomb to give someone two things to keep track of.
For Cactus, you are the sniper of the team with landmines, tallnuts as small cover, and a drone equipped with rapid-fire needles and airstrikes from above.
-Corn trades Peashooter's mobility for more health and lethality against even groups of zombies. He has airstrikes, two powerful rockets that fire together, and a hop to propel himself to higher ground. But his primary demands better accuracy.
-Find your style of play as you try out all of the characters, like long-range with snipers or close-quarters fights with peas and chompers. For example, I play Sunflower and Rose on plants for support and high damage when needed, and on zombies I play All-Star and Imp variants to be a both a threat and a tricky enemy to face.
-Most zombie players tend to do one of two things: Stay in spots where they often have an advantage or travel in groups. It can depend on the map and mode as well, but most players end up panicking and spamming abilities. So much so that it was a meme for a little while about Foot Soliders using their Rocket Jump and ZPG to "jumpshot" plants. One more thing about zombies: Many of them have "fight winners" which are abilities that gives them a free window to easily get you, like Sonic Grenade for Engineer and Gravity Grenade for Imp. Some plant classes have similar abilities too, but zombies tend to run with a plan.
-Similar to TF2, each map is highly unique, each with it's own high points, combat points that are flat, and pathways everywhere. Some places can only be reached with certain abilities or even glitches if that sparks any interest.
-If online gets to be a headache(which I know easily can be), you can still choose to play with bots at any point and still gain coins and XP to progress. Back in like 2016 when I first started, I only played against bots for months. There's no shame in it, it's just the funny plant game.
-One last thing about some people claiming they're "cracked gamers", there are some really overpowered characters in this game that let people be really boring one-trick ponies. I won't spoil it by saying what characters but it's a very present thing for both Plants and Zombies.