Choosing the right program for video editing
Your goal is best accomplished with Premiere Pro!

They are actually completely different, though I didn't see the difference until I learned them both well.

Adobe Premiere Pro:


Clip video and audio together...
(Mix audio, mix video)...
Color Correct
Add nice transitions...
Add many different effects, with animations and keyframes...
easy.


Adobe After Effects:


Add explosions
Add other special effects
Add 3D objects
Add any 2D effect you can imagine
Color Correct to balance your effects (though the last color correction should be done when compositing in Premiere Pro)


Any professional DAW: (Only do this if you are intending to make a blockbuster.)


Make the raw video in a video editing program, and bring it over here to add the audio.
Do all the audio here.


Vegas Pro:


Mix audio (it was originally made as a DAW.)
Do a little bit of Adobe Premiere Pro stuff...
Do a little bit of Adobe After Effects stuff...
Do a little bit of DAW stuff.
easy.


That's it. Do the special effects in After Effects, and all the clipping and color correction in Premiere Pro. If you're new to video, then Vegas Pro is easier to do much of what you can do with Adobe. But when you've learned a bit, Vegas will be a obstacle in your way of creating what your imagination says. And as you already know After Effects and Premiere Pro, then you're good to go!