* FNV4GB: Runs New Vegas with large address aware enabled so it can use a 4GB address space.
* New Vegas Script Extender: because almost (it seems) everything that isn't the vanilla games depends on it.
* One Tweak: technically a Skyrim mod, and more technically a Script Extender plugin, it works with NVSE. I use it for windowed full screen. Much more stable than the other windowed full screen hacks that I've tried.
* NVAC: Another NVSE plugin, it catches some of the memory errors that cause CTDs (crashes to desktop).
* TTW Fixes: This merges the FO3 Unofficial Patch and the Yukigachi Unofficial Patch (YUP) for New Vegas for use with TTW.
* MCM: The Mod Configuration Menu. Many mods use this which makes it a requirement.
* Zan AutoPurge: This one clears cell buffer caches to reduce inventory slowdowns and some types of CTDs. I just started using it so I don't know how useful it will be.
* DarNified UI NV: DarN's UI for New Vegas. Makes the UI a lot more usable with keyboard and mouse.
* SaveKey: A mod that provides a user-defined full (numbered) save hotkey.

I'd say that these are essential, the bare minimum. I have about 50 plugins in my load order not counting the game masters. These are the ones that without which I wouldn't try to run the game.

If you're still wondering what is Tale of Two Wastelands, it is a tool and some support plugins for running Fallout 3's content in the New Vegas engine. Essentially, it turns Fallout 3 into a gigantic mod for New Vegas. Thirty-odd hours into my current play and I'll say that the conversion is worth the effort.