Yes, you do need a custom firmware to run the games. 1.50 is mainly used for all of the homebrew stuff that was built around it. To play psx games at all, you need a custom firmware that has the features of at least 3.03. To play psx games well and with best compatibility, you need to upgrade to somewhere around 4.01 m33-2 and obtain the program known as popsloader. If you use Google, you can find guides on where to obtain these and what to do with these.
What is important though, is that you leave your 1.50 psp AS IT IS. DO NOT PRESS THE "UPDATE" BUTTON IN THE MAIN MENU!!! If you don't have all of your files and stuff in order, you may end upeither bricking your psp, or preventing yourself from making a Pandora Battery and Magic Memory stick. Since you have a 1.50 psp, you don't NEED the PB and MMS, but they are good to have in case you ever mess up and upgrade your PSP too far or brick it. Again, you can learn and obtain all you need on Google.
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