I'd suggest a Super Slim SCPH-9x, which is the last model of the PS2 line. The hardware on this particular model is decently designed not to fail, and it has an internal power supply. Unlike the regular Slim SCPH-7x, which desperately needs a laser diode fix for certain models and has an external power brick. Or even the older fat models, where each has its own issues... I think from the fat line, the SCPH-5x is the most reliable.
My SCPH-9x plays games fine in vertical, but some game types (PS2 blue CD-ROMs as far as I remember) make the drive vibrate bad, so I stay with horizontal.
I got mine modded to play PS1 and PS2 games from all regions. For PS2 Macross, the great PS1 library of Konami shooters, as well as the occasional PS1 puzzle game like Taisen Puzzle Dama and Puyo Puyo Sun.