PSP has a hardware decoder for h264/AVC video which is the same video codec used in Blurays and most digital broadcasting. It delivers high quality video at low bitrates and generally much better than competitors.
For audio it uses AAC (Advanced Audio Codec) which is again one of the best audio codecs out there and most content providers use it for high quality audio at low bitrates.
As x264 (free h264/AVC encoder and generally considered as the best) is still advancing, we now have the chance to use much better video at low bitrates for our PSPs. I will use HandBrake front-end which is available on PC/MAC/LINUX for this tutorial, but you can use any x264 front-end or even use command line interface.
First get HandBrake here: https://handbrake.fr
After installing, on main screen, go to Options>Import to import the psp Preset i uploaded here: https://www.sendspace.com/file/w12ju4
Go to Tools>Options>Output Files>Default Path to choose the output directory. You can use your "PSP's memory card drive letter"/VIDEO folder if your memory card is plugged to your PC. Or you can just copy the contents to your PSP later.
After that, you can just drag and drop the file you want to encode into HandBrake, click Start, you are ready to go. Your encode will be at 480x272 if your source has higher resolution than that. If not, its width and height will be rounded to the nearest multiple of 16 for compatibility reasons.
If you want to do batch encoding, choose Source>Folder to choose the directory of your source files. After that choose Add to Queue >Add All and then start the queue.
That is all, after your encoding is done, just copy the content and enjoy your videos. Continue to read if you want further info.
Explanations, Tricks, ETC.
Video
If you want to have more control over the settings, let me explain them.
I made the video settings so that you will have very high quality encodes at relatively large size and a long time. If you want, you can lower the video quality and both save space and reduce encoding time.
At the Video tab, there is Quality Section. I chose 18 which is nearly identical to the source. You can choose up to 21-22 without much lowering picture quality and have lower file sizes. I don't recommend higher values as they will make the picture much worse.
Other than that, at the Advanced tab, you can choose Hexagon (Default) for Motion Est Method for faster encodes, also you can reduce Subpixel Motion Est from my default 11 to 7 to drastically decrease encoding time. Both will have a negative impact on quality. Also you can choose lower Maximum B Frame values especially if your source files aren't cartoon/anime. 3-4 should be fine.
Audio
If your source file has AAC audio, you can choose "AAC Passthru" codec at Audio Tab. This will save you the hassle of converting audio and give you high quality audio. If not, you should choose a AAC codec to convert audio. AAC (CoreAudio) is your best option, but unfortunately it is only available to MAC users. If you are on PC or Linux choose AAC (FDK). If you care about high audio quality choose 160 kbps, if not you can go as low as 96 kbps.
Subtitle
Unfortunately PSP doesn't support soft-subs. It means you have to hard-code subtitles into your video if you want them. Go to Subtitles tab, choose the subtitle in your source and tick the burn-in box to hardcode them. You can also import a .srt file if you choose Import SRT option.
Miscellaneous
PSP can decode resolutions which both height and width are divisible by 16. Also both height and width should be smaller than 480x272. You got some exceptions for that though. PSP can also play 640x480, 720x480 and 720x576 values. With Tv-Out PSP can output 720x480 video at full resolution. So if you want to have your encodes playable with your other devices too or you use Tv-Out, you can choose one of the resolutions above.
Best of the Best
There are a few more things for increasing video quality, be warned, these will most possibly only aid your OCD.
As i have already said, PSP can play 720x576 video. As the PSP screen has 480x272 resolution, you shouldn't see any benefit from resolutions above this. But no, in fact you do see benefit, even though it is not much. PSP converts YV12 colorspace to RGB before outputting to LCD. PSP isn't very good at that conversion and higher resolution input will help the PSP do better conversion. So you can encode at 720x576. The quality increase will not be much but file size increase will be a lot.
You can also try increasing Motion Est Method and Motion Est Range, though encode will be much slower and your gain will be minimal.
Unfortunately you can't enable Weighted P-frames, Pyramidal B-frames and 8x8 Transform. Also you can't use more than 3 Reference Frames. PSP won't play the video if you do.
You can always try other settings and read about x264 encoder properties.
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