No.
Most machines have insufficient memory. 1.25 GB RAM (maximum on many) is just not enough, even for just basic surfing these days. If you have 2 GB RAM then it's OK, but to get 2 GB in an iMac means disassembling the thing, which is a real pain. The G4 iMacs use one DIMM and one SODIMM, but the DIMM is internal and very hard to get at. In fact, Apple considers the DIMM non-upgradable. Not recommended for the average user. On the iBooks, 1.25 GB to 1.5 GB RAM is the absolute max, since 256/512 MB is soldered to the motherboard and there is only one SODIMM slot.
Can't put SSD in these. They use IDE drives, and the drives are very slow. This makes the lack of memory even more problematic, since the machine pages to disk fairly frequently. SATA -> IDE adapters for SATA SSDs generally will not work properly.
The browsers are no longer updated for them. Only the really old versions work on them, so there are many compatibility issues. Don't expect to do your banking reliably on one of these. Also, HTML5 is a problem, and these Macs have no hardware h.264 decode support either, and the CPU is way too slow to decode it in software.
Watching a video is a major problem. The standard these days is h.264, and as mentioned above, that's a big problem for these machines. Playing even a standard definition h.264 just gives you a slideshow.
Hardware h.264 decode support didn't really appear in the lower end laptop models until about 2009, utilizing the GPU, in machines with Core 2 Duo, but not all Core 2 Duos have it. Luckily, most Core 2 Duos are fast enough to decode HD h.264 in software. However, personally, I would not buy any used Mac unless it had hardware h.264 decode support. Watching a 1080p h.264 video on a Core 2 Duo without hardware h.264 support is sometimes a problem, and puts the fan into high speed mode - loud. 720p usually plays fine, but with that loud high speed mode fan.
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So, if you don't like anything from the last 8 years, then probably the best you can do is get a Core 2 Duo iMac from 2007 or 2008. This would be a shiny aluminum one. Or maybe a 2008 15" MacBook Pro or something.