I like magic-heavy parties. Not necessarily pure magic parties, but magic-heavy ones. For MM8, the party I like is priest, necro, dark elf, vampire, and dragon, which gives me access to all forms of magic and all the monster skills. I don't start with a dark elf, because Cauri is so good and you can get her into your party quite quickly. The vampire is my least favourite of the final party, so I don't want to start with one of those, and in the legitimate game, you can't start with a dragon. That leaves priest and necro, and I tend to alternate those as my start character.
I think Invisibility works anywhere until you either attack something, or something bumps into you.
The Fire plane is hard work, but as long as you can kill one monster without losing characters, you can do it. Use ranged spells and ranged attacks to chop the welcome party down one by one, and stay within range of the portal so you can dive back through to rest and heal in safety when you get badly hurt.