The SE had QuickDraw. What it lacked was Color QuickDraw which is something the SE/30 and Classic II had. The older machines lacked that. Hence why Quicktime and some games won't run on an Classic, SE or older machine. Which is too bad. Kinda hoped Wolfenstien 3D would run on my SE, but looks like an SE/30 is the minimum requirement for that game. 
Some of the more graphical oriented browsers (ones that could display image content and whatnot) certainly would have needed Color QuickDraw (there's also 32-bit Color QuickDraw. Not sure if the SE/30 has this or not?). Hence options are quite limited for the SE. The browsing experience on today's internet is going to be terrible either way, but I suppose the SE/30 with it's more fancy version of QuickDraw can perhaps display a few images on a webpage. God knows how they will end up looking after being dithered down to 1-bit monochome. Unless you have one of those mythical SE/30s with the Xceed Grayscale adapter installed where some pages may actually come out looking ok. In which case you are very lucky and I hate you...
Not to mention some of the more advanced browsers also needed a 020 or better CPU. The old 68000 just won't cut it for those even if it had Color QuickDraw. The SE/30/Classic II had a 030, which ran quite a bit more stuff then the SE and older machines. I hear an SE/30 is basically an LC II without the 16-bit bus limitation. Which is pretty bad ass. I suppose if you want to relive the LC II crippled experience then the Classic II would be for you. But the SE/30 is a beast.
Some of the more graphical oriented browsers (ones that could display image content and whatnot) certainly would have needed Color QuickDraw (there's also 32-bit Color QuickDraw. Not sure if the SE/30 has this or not?). Hence options are quite limited for the SE. The browsing experience on today's internet is going to be terrible either way, but I suppose the SE/30 with it's more fancy version of QuickDraw can perhaps display a few images on a webpage. God knows how they will end up looking after being dithered down to 1-bit monochome. Unless you have one of those mythical SE/30s with the Xceed Grayscale adapter installed where some pages may actually come out looking ok. In which case you are very lucky and I hate you...
Not to mention some of the more advanced browsers also needed a 020 or better CPU. The old 68000 just won't cut it for those even if it had Color QuickDraw.
The SE/30/Classic II had a 030, which ran quite a bit more stuff then the SE and older machines. I hear an SE/30 is basically an LC II without the 16-bit bus limitation. Which is pretty bad ass. I suppose if you want to relive the LC II crippled experience then the Classic II would be for you. But the SE/30 is a beast.