All PSPs on all firmwares are hackable, but to different extents:
1000s and early 2000s can run custom code right from when the power is turned on (even from a memory stick if you use a Pandora battery)
Street/E1000 cannot be downgraded below 6.60, so it requires CFW to be manually run after a full poweroff/reboot, still it's a matter of less than 10 seconds
All other models (2000 ta88v3+, all 3000, all N1000/Go) technically can't have custom bootloaders, BUT there are exploits in certain firmwares (6.20?) so the console can be downgraded to get CFW at boot; even arguably better, it can be partially downgraded (Infinity) to get autobooting 6.60/6.61!
Note that Go uses "M2" instead of standard Memory Stick Pro, which is only available up to 16 GB and is expensive (but you have 16 GB internal storage which is enough for a passable amount of trimmed games and some music)