If you want a quick game that plays dead simple but is loaded with strategy and risk taking then I can’t recommend Coloretto highly enough. Everyone I’ve introduced it to loves it.
Lords of Waterdeep is a pretty great D&D twist on a worker placement euro-style game.
As for D&D I think it’s pretty safe to just jump into 5th edition. You can probably start with the Starter Set as it does some of the more intimidating heavy lifting for you (character creation and adventure design) so you can get a feel for the game before making choices that could impact the characters or campaign for a long time. Don’t be afraid to play fast and loose with the rules and fudge some rolls since 5e can be pretty deadly at lower levels.
As for more board games, Board Game Geek is an obvious starting place but I also recommend Shut Up and Sit Down.
