For NG OSes, I'd stay away from the classic Amigas. A better performing NG system can be had for much less than the cost of a CSPPC.
Agreed. Insidious611, a PPC Mac running MorphOS will be your cheapest, most powerful, most feature-complete (given the needs you mentioned) option. You may also want to consider AROS for x86 hardware - it's free and comparable to MorphOS in terms of features. Not sure if MegaZeux is available for those platforms, though.
MorphOS has a free trial. It's fully functional, but slows down after about 30 minutes. After a 6 second reboot, you're running at full speed again. A keyfile to disable the timeout costs 111 Euro at the moment (purchased from within the OS). Add in about $300 (probably less) for a Mac and things are still pretty affordable. QEMU isn't an option. The version of MorphOS that ran on it is an old internal experiment that was never publicly released.
Building up a PPC Classic system will be extremely expensive and will probably take a long time - the needed parts aren't for sale very often. You'll likely be disappointed with the performance. It definitely can't handle web video.
OS4 requires a large upfront investment. The custom hardware is very expensive due to low production volumes. The web browser and video players are far less developed than on MorphOS, but there have been some good improvements lately to bring them more in sync.
I don't know much about the latest with AROS, but it has a cool version of UAE that provides 68K compatibility in a way similar to MacOSX's Classic Environment.
You may want to consider a simpler Classic 68K Amiga alongside a MorphOS or AROS box. The 2 together will probably still be cheaper than a Classic PPC or OS4 machine.