To my understanding and attemps, system will get world as well, plus some extra packages that make up the system.

I've got two three suggestions for this.
1. Make a gentoo install on another computer that's broadband and keep the whole /usr/portage directory, then proceed with the install on the other computer
2. Make the gentoo install on your dialup computer, but then burn the /usr/portage directory on a disk for subscequant installs.
3. Make a stage3 install, then slowly download all the files and make it a stage1/3 or stage2/3 install, whatever pleases you.

I apologize for not making my post more clear. I don't have this machine I am building where I have a fast connection to the internet and I can't bring it the one I am using right now. Without having a same class machine running Gentoo, how do I go about downloading the distfiles?

Thanks