Which one should I use before I start installing my mods? Which one is more preferred?

Use of Wrye Bash will be mandatory if you install mods which alter leveled lists, it's needed to merge them. Might as well use from the start.

I think you will find serious old school gamers prefer Wrye Bash and the people who are not as "old school" but still really serious about their modding will prefer Mod Organizer.

The advantage to NMM is that it is easy to learn how to use and it will tell you when an update for one of your mods are available on Nexus. It is more for people who don't want to spend the time to learn either Wrye Bash or Mod Organizer, and need a reminder when updates are available.

Both Mod Organizer and Wrye Bash have features that NMM doesn't. Wrye Bash and Mod Organizer each have different features that the other doesn't.

Mod Organizer makes it a littler easier to switch between different installs than Wrye Bash, since Mod Organizer keeps your Skyrim folder vanilla and adds mods at runtime through a virtual folder based on pre-selected "profiles". But only Wrye Bash does the bashed patch, so if you want to merge levelled lists, you will be using it, regardless of whether you are using either NMM or Mod Organizer.

Edit: Although there are alternatives to a bashed patch. Mator Smash and such, I cannot really comment much on those since I don't know much about them. I am personally a proud and happy Wrye Bash user.

But I don't currently use a bashed patch for Skyrim because one of the mods I am using (Requiem) includes its own merged patch that provides bashed patch functionality.

I never got the hang of merging level lists. I have so many questions for it, like do I have to know which mods needs level listing merging or can I just do it on all my mods and it won't cause any problems?

If you use the latest version of Wrye Bash and LOOT, then Wrye Bash will tell you what to merge automatically. What you do is activate all your mods and sort them with LOOT. Once you have everything like you want it, you go into the Wrye Bash mods tab, right click on bashed patch 0.esp and select rebuild bashed patch. Wrye Bash will ask you if you want to deactivate certain mods to merge/import them, just click yes -- you can trust Wrye Bash's recommendations here and htis will reduce the number of active esp files in your load order, allowing you to use more mods before you hit the 255 cap. Then Wrye Bash will bring up a big menu with a lot of options. You want to put check in the box for merge leveled lists and check anything else you want the bashed patch to do. Most of the teewaks won't work for Skyrim, so I would probably just make sure there is a check in merge leveled lists and leave the rest blank/ or whatever Wrye Bash does by default is usually okay. Then click rebuild patch.

The way Wrye Bash determines what to merge is a system of "bash tags" that are imported into Wrye Bash when you run LOOT. These "bash tags" tell Wrye Bash what to do, so you don't really have to worry about it. But you can manually add "bash tags" if you want. There is more information on that in the Wrye Bash readme. Delev and Relev are the most commonly used tags if the mod alters leveled lists. Before building your bashed patch, you can view the bash tags in Wrye Bash by clicking on the mod and looking in the window to the right for the bashed tags associated with the mod.

It all sounds a lot more complicated than it really is once you start using Wrye Bash. Here is a link to the pictorial guide that will make learning Wrye Bash much easier. http://www.nexusmods.com/skyrim/mods/36189/?

EDIT: As far as which mods need merging, in general any mod that adds loot or enemies will need to be merged into a merged patch like the bashed patch that loads last in order to make the changes from that mod are distributed into the leveled lists and you see them in game. Without a bashed patch, if you have multiple mods that affect the same "entry" only the last mod loaded will have effect in game. The bashed patch gets around this limitation by merging all such changes into a single patch that loads last, so multiple mods that affect leveled lists can be implemented in game.

Well i consider myself old school in the fact way back in morrowind when it first came out..we didnt have mod managers but we had to do everything manually but on the subject i prefer NMM.

Well, each to his (or her) own, and I certainly did not mean to insult your old schoolness. Many consider Wrye Bash "old school" because of its user interface appears dated and even sort of retro, unlike the polished modern looking interface of Mod Organizer, so that's why I said it was for old school gamers.

But on the topic at hand, it might help the OP decide which to use if you explained why you prefer NMM to Wrye Bash . . .

Wrye Bash is the better choice in this case. If you're installing mods that have loose files, NMM won't handle overlapping assets correctly. Which hasn't changed since OBMM.