Essentially, you need a version 1.50 firmware psp or anything up to I believe 3.03 (or 3.01 can't remember for sure) but no higher. If you get anything after a 1.50 or up to 2.80 you can run a downgrader to return to 1.50 even on the newest psp motherboards without the need of an unpatched Grand theft auto LCS umd game. With a a psp > 2.81 but < 3.03 (or 3.01 whichever it is) psp I believe you need upgrade to the respective firmware be it 3.01 or 3.03, check the faqs to be sure. After that you will need to run the downgrader for that firmware with the unpatched GTA game.
The bottom line is that you need something that you can downgrade to a 1.50 psp from which you can upgrade to DA's custom firmwares which allow you to play you own psx games if you so choose. 1.50 will run all homebrew, but does not have the features of later psp firmwares, while DA's custom firmwares include the most of the newest features of the psp and the homebrew and psx functionality. You can play snes games with a snes emulator made for the psp, check dcemu's psp site and look under the emulators for psp section on the left side to get yourself started, I recommend SnesTYL or whatever it is called. As of right now the most current firmware is 3.30 and the most current custom firmware by da is 3.10-OEA'. The reason I mention this is that whenever new games that require firmware 3.30 come out (of which there currently are none) you will not be able to play them until DA comes out with his next custom fw supporting 3.30. Or you can downgrade back to 1.50 and upgrade to the official sony 3.30 but lose all homebrew functionality. Usually DA is pretty on top of things with his custom firmwares, and they are out before any game requires the newest firmware. However the possibility that he may discontinue his work is always a possibility and something to keep in mind. But like I said there is a recovery feature in his custom firmwares which allows you to return to the official sony 1.50 firmware and upgrade to the latest official sony firmware from there.
So to recap get a 1.50 psp if possible and upgrade to da's custom firmware via the faqs for psx iso, official umd, and all homebrew capability, or if not get anthing under a 3.01 (or 3.03 like I said check to be sure) and downgrade via the appropriate method to 1.50 and upgrade to da's custom firmware. Da's custom firmware's have a recovery mode so you can always go back to the official firmware (although on downgraded ta-082 and ta-086 motherboards I have heard of people not being able to upgrade to the latest official firmware, and I'm not sure if that was solved or not). For me thest best price per space range of memory sticks was a 2 gig and it stores a lot of stuff. I think you can get a 4 gig nowadays on sale at places like Fry's or Circuit City for a pretty decent price and considering the 8 gigs just came out they should continue to get cheaper. Just don't buy off ebay, you will likely get a cheap counterfeit ms pro duo and this can brick your psp if you use it to downgrade. For the downgrader and DA's custom fw's I would recommend having at least 256 mb just to be safe, but you may as well get a bigger one if you plan to play psx games, at least 1 gig.
And just to be clear, if you want to do homebrew, play psx games, etc. for the love of all that is good and holy do not upgrade your psp. Period, unless it's a custom firmware upgrade. With official firmwares, anything beyond 1.50 cannot (for the most part) do homebrew or psx games at all. With custom firmwares, you can play all of the newest games, and play homebrew such as a snes emulator and play psx games via pops the official sony psx emulator for psp. So keep in mind sony's official firmware upgrades = bad for homebrew enthusiast, DA's custom firmware's = Pure homebrew bliss plus full psp functionality minus the location free player, korean font, plus recovery mode to recover from bricks and return to official firmwares if you so choose.
I hope this all made sense and that I didn't just scare the crap out of you, and that it helps you. If you have any more questions I or surely someone else will be glad to help as best as we can.
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