Hello and Welcome.
No need to hardmod a Gamecube to make it region free, you can access to SWISS via Game Save exploit, then any region GC can output any display frequency, from RF modulator to HDMI (provided you hve a DOL-001 with Digital AV), and RGB for PAL ones and S-Video for NTSC hardware.
You should force 60Hz modes on PAL games as soon as they support it natively, as most of them are just frameskipped when run in 50Hz, and can result in headaches and seasick when playing fast moving 3D games.
Why go for p instead of i is that modern displays don't consider 240/288 lines is enough to interpolate to their higher resolution, so they prefer to blend two successive frames, totalling 480/576 lines, ignoring about temporal issues such as blur it can cause. Progressive scan with double bandwith provide this high number of lines for each frame, so TVs can straight interpolate and allow more crisp picture. You can also get this higher quality picture at the expense of the framerate, with the "sf" modes in SWISS, as long as the games supports it, without the need for a Component or HDMI cable that are the only way to get real 480/576p modes.
If you have a CRT, stick to RGB-SCART cable, that's the way to go, but if you want to go digital, don't bother buying digital to analog cable (OEM Component cable), GCVideo HDMI dongles are way cheaper and are digital from end to end. If you feel like you really need component out, consider buying a Wii, which may get cheaper thant the OEM GC component cable alone. GCVideo can upscale 480i to 480p but this feature only has seldom uses.
All the bulls…t you read all around was mainly eluding what magic SWISS is capable of:
Any game can run on any region console, from either optical drive or SD card.
Any game can be forced to either 480p or 576p according to what framerate it originally supports.
Almost, if only everybody was able to read english.
You can dig this forum to get more in-depth explanation on how GC video generation works, such as internal to external video scaling and converting. We have better see Extrems using his freetime to improve SWISS than answering questions that have already been debated.
Look at what is my hardware in my signature, and watch my videos to see it in action.