I heard it was the old PS2's that overheated and had laser problems, and that the new PS2's have no hard drives and thus need memory cards to save anything. Makes me not want to get a PS2 at all...
The older PS2's did have laser problems... newer versions have been fixed, including the newer slim PS2. I've heard the newer ones overheat online, but ppl I know that have it have never had the problem. I've owned 3 different "fat" PS2's and never had one overheat, even after longgggggg game sessions.
PS2's never came stock with a hard drive, so you needed a memory card anyway, so I'm not really sure what you mean there. You're thinking about an xbox. In fact, even with a hard drive installed, I don't think you can use it as a memory card, but I may be mistaken there since I've never tried to do it. I have HDloader on my PS2 and certainly haven't seen an option to turn the HDD into a memory card.
Don't get a PS2 if you don't want