When I first entered New Reno, I pretty soon joined the Salvatores and did their missions. As a result, first I got attacked on sight by the puritan family (Wrights, right?) an wiped them out. Then later another clan (The one with big and little Jesus) followed. I have not killed them all but their guards in front of their casino, who attacked me.
Now I wonder if I have missed a lot of the storyline and what could happen in NR storywise that would maybe make things easier for me. Have I made things unnecessary difficult for me? Or is it just one of the many cool ways to beat the game? My character is a sweet-talker medic kind of guy with reasonable small weapon skills and a good crew to cover my back.

Each of the families offers you some minor side quests, so you miss out on those and the resulting XP. Wiping out the Wrights means you miss out on looting a nifty military base and picking up an unusual NPC. Nothing you really need to finish the game, though you can find a Red Ryder LE BB gun. A different Wright quest can get you a unique and powerful melee weapon, but not something you really need.

Having the Mordinos turn hostile interferes somewhat with milking the maximum XP from the Jet antidote quest and causes it to take longer.

Fun fact: It's possible to get "Made Man" status with all four crime families in New Reno. Only the last one counts, but they all show up on your status. There is also a specific way set up in the game to assassinate each of the bosses. The one for Salvatore is bugged, it still works but not the way it should.

You should not worry about parts of the game you might have missed. There's no way to do and see every single thing in the entire game in a single playthrough anyway (although as CharlesEllis said it is technically possible to join all the New Reno crime families in one game). Next time you play, make a different choice with a different kind of character.

Thank you. I am somewhat a completist, trying to get most out of a game in one playthrough, even if it takes me ages. The guy who opened every chest and sold every little arrow fired by a kobold in Baldur's Gate in order not to misss one coin, who tries out every branch of a dialogue tree etc. Needless to say, I need to let things flow a bit more in order to enjoy games such as Fallout or Planescape:Torment.

Well, you can still play that way...but you're not going to be able to get everything with one character. It's a testament to just how much material there is in the game. I've been playing it for a long, long time and I still find new things now and then.

I'm assuming you haven't tried playing a character with very low Intelligence, for example. They have completely different dialogue.

I want to try this sometime. Dumb like a monkey, still he is the chosen one.