In today's hobby, you are basically talking about running conventional trains and/or command control trains. Conventional trains, like your 1950' set, run on track powered by a simple AC transformer connected to the track and speed, direction, bell, whistle functions are typically controlled by the moving the throttle up or down or the buttons on the transformer.
Command control trains are basically wireless operation where the transformer simply supplies the power to the track and other train functions are carried out via a wireless signal to the engine from some type of remote controller or from an app on an electronic device such as a cellphone, Ipad, etc.
Like Dan said, if all you want to do is run conventional trains, all you need is some track, some wire and a transformer. Of course, you will have to decide which track and switches to buy (old school tubular, modern 3-rail like Gargarves, Atlas, etc. or molded roadbed like Lionel Fastrack or MTH Realtrax) and which transformer to use ( both Lionel and MTH make entry-level transformers like the CW-80 or Z-1000).
I would suggest that you try an entry-level command control like a Lionel LionChief engine that will run on a basic layout with a simple emote or bluetooth and see how you like it compared with your conventional train. I would also recommend that you start by picking up a new 2021 Lionel catalogue at your LHS and look through it to get an idea of what's available and also speak to them to get ideas.
Once you get your feet wet, it's like anything else and you'll pick up the lingo in no time.