What software is used in Hollywood for special effects and video editing
For video editing the Hollywood standard is AVID, however smaller production houses and indie filmmakers tend to use Adobe Premiere. The nice thing about Premiere, in your case, is that it dynamic links with After Effects where you can do motion graphics, composting and basic visual effects such as green screen removal among other things. To explain these keywords would be outside the scope of this website, but dynamic link basically means you can seamlessly go from your edit to your vfx without rendering intermediates.

Nuke is difficult to learn, and requires you to have a foundation in visual effects. Nuke is not an NLE, so it only does visual effects. The benefit of using it is due to its collaborative nature as well as node-based non-destructive structure.

This all probably sounds like garble to a starter, so I would suggest starting to learn Adobe's creative software, and follow some tutorials from http://www.videocopilot.net/.