If I were you I would do this. Note that you can install a perm CFW but that would involve downgrading and I myself don't know all that much about it and feel a little uneasy about showing how to do it. If you would like to downgrade I'm sure someone will come along and show you how if you would like.
But this CFW is just as good as the PERM CFW you will just have to run the LAUNCHER for it everytime you turn the PSP on from the OFF state.
First you need to update to OFW 6.60 and then install CFW, here is how you can do it.
You can either update to 6.60 OFW by system update or you can manually download it yourself. If you do system update with the psp skip these first steps.(also skip if your already on 6.60 OFW)
1) Download and extract the 6.60 OFW and keep it where you can find it: 6.60 OFW (PSP Go!) - Downloads - PSPMOD.com - PSP Forum, Hack PSP, PSV Hacks, PS Vita Hack, PSVita
2) Go to USB connection on the psp and pull up the drive that the psp is connected to on the computer.
3) Now open the PSP folder and then the GAME folder and then in that GAME folder make a new folder named UPDATE (all caps)
4) Put the 660 OFW EBOOT in that update folder and then exit USB mode.
5) Go to GAME in the psp XMB and run it.
Now to install CFW.
1) Download the CFW from this link: 6.60LME-1.6 - Downloads - PSPMOD.com - PSP Forum, Hack PSP, PSV Hacks, PS Vita Hack, PSVita go to the GAME folder just like you did in above steps. (See step 3 above if you don't know how to find the GAME folder)
3) Delete the UPDATE folder because you will no longer need it. (Only do this step if you did the above steps for installing OFW)
4) Place the Launcher and the Installer files in the GAME folder.
5) Exit USB and go to the GAME in the XMB and run the INSTALLER and then the LAUNCHER
Since this is a Lite CFW when you shut down your psp it will be wiped from the RAM so when you reboot you will have to run the LAUNCHER again.