If you are looking to ease into Euros, I might suggest the BGA ‘casual games’ category - generally light on rules/complexity so that may help.
Honestly the site has almost a historical overview of ‘gateway’ games through time - catan, ticket to ride, carcasonne to splendor azul and such as was mentioned above.
I believe the most popular game there now (this info is posted somewhere on the site…) is ark nova, not a place to start though.
As to real time vs turn based, the main difference is essentially how long before you are ‘out of time’ (minutes vs days). At that point other players can kick you out and your ‘reputation’ is damaged - some people will not play with people with bad reputation. Even when setting up a game you can exclude players on this criterion.
I just posted an innovation game exclusively to the qt3 group. That is another way new games can be limited in their options. (I realize now I set up the game with expansions… if someone wants to play without , let me know or just invite me directly).
BGA has a ton of options yet has its detractors for a variety of reasons. Some (including me) prefer the always free always asynchronous Yucata.de (fully English despite German domain name - fully German too!)