With slide tool you need to use it to pull gear levers to make the disc tray eject, then again to close it. You run the risk of breaking these extremely thin pieces of plastic, or worse, doing damage to anything inside that part of the ps2; including the laser.
with fliptop, there is no risk of damaging anything, unless you spill water into the ps2 when its open, but then if you keep water near your ps2, then that'd be your own fault!
I would recommend buying from a proper console modstore, NOT eBay. After all, you wouldn't buy a DVD from a grocer would you?
I also recommend DVD-R, as all ps2 can read them, but some ps2's have issues with +R. Also, you don't need to booktype -R before burning as they're already recognised as DVD-ROM, but you do with +R, and your burner may not support booktyping. Just make sure they're a good brand, such as RITEK G05, Verbatim, Sony.
There are other methods, but you're more restricted to the games you can play (size-wise), and you'd still need a way to swap discs.
Just get a Swap Magic 3.6 & fliptop case combo. There's plenty of deals out there, and it won't cost you that much.
Best Source For Your PS2 Needs. Always
first with new PS2 DNA$ Disc IDs - Be 1st to get your backups online!
Our Latest IDs: Test Drive Unlimited(PAL), Snooker 2007(PAL), UEFA Champ League 2006-07(PAL), MVP 07 NCAA Baseball(US), CollegeHoops2K7(US), ArenaFootball:RoadToGlory(US)