The 2nd game is much better than the first imo. So i'd play the 2nd one, don't need to play the first one. There is a simple story in the first game, but these games aren't really about story, and the ones they do tell aren't very good imo. Think of the games like mmos and how much story you might get from a random WoW fetch quest and that is what you have here. Oh and the first game doesn't have multiplayer, only the 2nd.
The games are basically if you put EA's The Sims into a Zombie Apocalypse. You build a community and a base, and try to survive. In the main game mode, called "the Campaign". You start out the game by selecting 3 random characters (or 3 characters from previous communities), with specific traits, and then a map. There are 4 maps in this mode, and you can move your community between all 4 if you want. I'd definitely start with the one they added recently, Providence Ridge. Its more streamlined for new players. You gradually recruit more characters with their own special traits and build up to bigger bases. The game has permadeath, so if a character of yours dies, they ain't coming back.
You can complete a map and see the end credits by destroying all of the "blood plagues" on a map and completing all of your community leader's goals (called Legacy Goals I believe). You'll get some perks for future play throughs. For example by completing the "Builder" leader goal, you get free power and water for your base. And the characters in that community can be used in future playthroughs. Starting a game with a leveled up character and some of the perks is quite nice.
Of course, you can ignore those goals and try to survive as long as possible. People like to do a 100 day challenge. The game can be quite rough, especially on the hardest difficulty. Make one small mistake and suddenly you are in a world of trouble.
The 2nd game mode is "Heartland". This was DLC that was released last year, which is included in the Juggernaut Edition. Its set in the first game's map, and has a simple story like the first game. I didn't play it much, didn't quite like it. I have never found the story stuff in the first game or this game mode very good, but some people absolutely love it and begged Undead Labs for something so this is what they released.
The third game mode is "Daybreak". Its just a simple siege style game. You defend against zombie attacks. You can earn points in this mode to be used in the main game mode for a special trader if you want.
As for the coop in the Campaign mode, both of you will need to start a community in the campaign yourself first. Once you reach the base and claim it, should take like 5 mins if you skip the tutorial, may not be able to on first playthroughs, don't remember. You will be able to join other people's games with one of those characters in that community. The multiplayer is peer to peer, so it is hit or miss. Lots of people have complained about errors and dropouts so be warned. It works on a rubber band type system so the person that is joining the game can only get so far away from the host. And only the host can manage the base. So it will have limitations for the 2nd player. Its kinda like the new Animal Crossing in a way. But fun anyway.
As for recommendation, play the 2nd game. The mode "Campaign" and on the map "Providence Ridge" I believe that map is the default map now anyway, so it should dump you in that map after the tutorial. The game is on PC btw as well. Microsoft Store, Steam and Epic Game Store, and of course Game Pass for PC. So don't need to buy a xbox if you have a PC capable. Its cross-play between every version.
edit: and as for the graphic changes. They didn't do much. New lighting system and better road textures. Its certainly better than before, but nothing special.
Also for new players, I recommend looking through this guide:
Survive the zombie apocalypse with the definitive State of Decay 2 player guide. View and Download the PDF player guide here.
www.stateofdecay.com
and looking through the "how to play" section in the menu of the game when playing.
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