Sounds like you got it under control, but I work with this stuff all the time so I can't resist chiming in
I work on Macs and usually use Final Cut Pro or Avid so can't give you Premiere-related advice though
Like Wavex said, the stuttering is probably from your export settings in the old program. My guess is it did a bad job converting frame rates and used an older video codec. Sounds like your new app fixed that :thumbup:
(Note: my gopro files play at 27fps, which is very odd. I imagine older programs might not handle that smoothly)
In general, you want to keep the video either at it's native format/settings through the process, or convert it to something higher quality for the edit then export compressed videos from that. You will never get more detail than the original, but you can try to prevent further loss by bumping it up for the edit.
For exporting, since I'm on the Mac side, I usually use quicktime. Regardless, here are some tips:
If you want it to be a small file size, export it with a modern codec (H.264, AVC, MPEG4) at 320x240 but with a decent data rate (quality sliders at medium or better) and it will look fine. Experimentation is really the only way to find what works for what you want to do.
If this is something for youtube, I tend to use bigger frame sizes and deal with the bigger files to compensate for the compression that Youtube does. For the GoPro stuff, sometimes doubling the native frame size can keep it from looking soft after Youtube does it's thing. Be warned, 2x frame dimensions = 4x file size.
My usual settings are Motion Jpeg codec at 75%, 30fps, and then pick a frame size relative to what the footage was shot as. Keep in mind, I don't care about file size, so these often end up 100s of MB.
Stick with 29.97 or 30fps depending on your source. (15 fps will cut file size in half with a tolerable amount of choppiness, but our awesome motorcycle footage looks smoother when you keep it at the faster frame rate :thumbup

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While the high end video work can benefit from those monster graphics cards, they aren't necessary for most consumer programs that we'd use for these kinds of videos. If the application is designed for it, your video card can help when you are using effects (color correction, other visual effects) and speed up exporting certain formats, but their primary job is only to make the picture show up on your monitor.
The first bottleneck you'll run into other than space Will only happen when you start working with uncompressed and/or large HD files. Some hard drives can't access the data fast enough. (That's a whole other geeky post though

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Hope that helps you, or someone searching, but definitely look at
youtube's info.