What's the best approach to adopting 1.d4? As a long time 1.e4 player and short time 1.c4 player, I'd like to add 1.d4 but there are so many defenses.    I am considering the London system against things, while adding mainlines vs. all the various openings one by one.  Or is the Catalan a better start?
If you want to start playing 1.d4 you should as first thing have a look at some theory about the Queen's gambit declined, as it is the most natural (and historical) way to play 1.d4: even if you will not end up adopting it in your repertoire, it will give you a taste of the major ideas behind the queen's pawn opening (minority attack usually against c5-c6, occupation of c-d files) and a sense of where the pieces belong.

After you do so you should start preparing for precise defences to play against (as in every opening although White has the first move, the order strongly depends on what Black plays next): in this respect you might have a look at any online database to find what is played most - but to spare the time, among all the most often played are:


Slav defence
semi-Slav
Indian defences (at least King's Indian and Grünfeld)



  Or is the Catalan a better start? 


I myself do play the Catalan (when given the chance to do so) and therefore by all means I suggest you to look into it: it is however a heavy theoretical opening (from both sides) but it does provide White with a slight edge throughout the whole game (at best play).


  I am considering the London system against things


The London system is somehow more "natural" to play and it is lately gaining a lot of respect at high level (Carlsen and Aronian above all play it very often): you may find quite a few GM games to take examples from.

In general, as any other opening in chess, you cannot have your way around without putting some study into a few specific lines; however, there is a lot of free content online that you may surf, especially the Saint Louis Chess Club channel contains a lot of opening videos suitable for any level (according to me very thorough).