Hi MeMaria -
I'm not an expert on video codecs, but your phone and it's CPU, RAM limitations are a major factor in playback of certain video formats. If the specs you listed are accurate, that alone may in fact be the problem. Videos come in a variety of formats, such as .mkv, .MP4, .AVI, .3GP etc. You didn't list how much RAM (memory) your phone comes with, but seeing as it's a 600 MHz CPU, I'm willing to bet it's somewhere in the 512MB range which, paired together with a weaker CPU will not be sufficient to view most video formats, especially those from youTube or mkv containers due to the video compression rate.
I had the same problem with a similar phone; laggy audio, subtitles and sometimes no playback at all. After rooting, overclocking phone to 800 MHz, stripping bloatware and freeing up as much RAM as possible, I could get HD videos as well as netflix to play decently. But if you're stock, no root there is another way to get your videos to play but it involves more work.
There are video editing apps out there for your PC. I used Any Video Converter to reduce the video compression framerate as well as change the files to .avi format. Let's say the videos you downloaded play back at 30+ FPS (frames per second). If you reduce the framerate to 20-25 FPS your phone is more likely able to handle the playback. Reducing framerate will reduce video quality by some, and also reduces file size. It takes a few trys to get everything just right. My old LG Optimus was happy with videos converted to 23-25 fps using .avi format, using MX player (I think MX is best). I know it sounds like a lot involved but AVC is very easy to use once you play around with it for a bit. Your only other option is upgrade to a phone with stronger specs that can handle HQ video.
I hope that helps!