I recommend against a swap disc. I got one myself once, and I found it annoying. It's not that much more expensive to have your PS2 modified, and if you live in a reasonably sized city (100k or more), you should be able to find professionals who can do it for you.

When it comes to the PAL/NTSC issue, that still applies when you're running an NTSC game on a modified PAL PS2, just as it would if you had a real NTSC PS2. Nowadays, this isn't much of a problem anyway, because most new TVs can handle both signals just fine. Earlier, NTSC games would be in black and white, and you'd need a special kind of cable to fix the problem. If your TV is very old, you might need this.

You never have to pay for an emulator. One of the best emulators avaliable is free of charge (ePSXe).