Maybe use Spotlight to find a file named org.videolan.vlc.plist and remove it from the folder you see it in. Reopen VLC and see if it crashes anymore. This file holds all your VLC settings and if you want to keep them and this doesn't solve your problem then you can simply put the file back where you found it originally, replacing the newly created file, reopen VLC and have all your old settings. This probably isn't so much of an issue for you because it's such a new computer. 🙂
As for other apps crashing, maybe run Activity Monitor in the background (it's in the Utilities folder) to see if there's a process using up a lot of CPU or RAM.
FWIW, VLC is a pretty unstable app. It crashes quite a bit but we love it anyway. 😛