I'm thinking about getting a Series S but don't know what to buy for my first couple games.

I really only had Nintendo consoles. Is there anything you can recommend?

Just get Game Pass, hundreds of games you can play from the 360, XB1, and coming Series games.

As Noble said, Gamepass! It has tons of MS exlcusives you've missed on xbox one (and possibly 360). For games not on GP, Yakuza Like a dragon is a cool JPRG if you like those games. Speakin of JRPGs Gamepass has a slew you missed out on if you only had Nintendo consoles. Might help to hear what kind of genres you like to further assist.

Game pass aside, I recommend Lost Odyssey (not on game pass). 

What kind of game is it?

I have a wide range of tastes

Platformers, action and adventure, strategy, RPGs

Also question about gamepass do the game download onto the console and how long do I have to play them?

The games do download onto the console and you can play them for as long as they remain in game pass and you keep your sub active (How long they're in game pass isn't told to us but MS does tell us some weeks in advance if a game is leaving soon or not). 

Game Pass like everyone said but if you plan on only purchasing games and have only had Nintendo consoles you can't go wrong with Nier Automata Highly recommended.

JRPG. copy paste on your favorite search engine for info, but I'd go blind. 

I'm also going to recommend Yakuza Like a Dragon. Also if you get Game Pass and if you even remotely like racing games one of the first games you should try is Forza Horizon 4.