By all means, the Macintosh line won't be the earliest computers to connect to the internet.
Now there is also the small matter of what do you call internet? Do you mean the common IP/TCP protocols connecting over the world wide network? There is also usenets and BBSs
Technically if you want to find the earliest computer to do anything related to the internet, find an Altair 8800 (Or clone) with a telephone MoDem in it.
Like wise get a Mac 128K with a modem installed, however even the Apple 1 could theoretically connect to some form of world wide communications if you hook up a modem with it.
If your talking about IP/TCP, then you have two routes, connect to the internet, but good luck finding a webpage that will work with that, or connect to the actual internet and browse modern webpages.
The first option, grab the earliest Ethernet card you can find, and the earliest Mac or PC that will accept it, and there you go. Second option, your looking at a late 68k or early POWER Mac, but those will have a hard time connecting to most websites, and you will never get youtube to work on them.
The first macs that will REASONABLY connect to the internet is the G3 series, but there are few browsers that will run on them. Your best bet would be a G4 or G5 machine, those could pull decent internet, and most of them look good.
As for looking good, that is a question best answered by yourself, we can't help you with that one, you'd just get opinions.