Yes, forget the "Commodore" machines -they're just bog standard PCs with a blue wallpaper and a doubled price tag. They are nothing to do with Commodore from the 1990s, they just bought the name.
An A1200 is good, but beware as they're all getting older and they're expensive to upgrade to a good standard.
A cheap AmigaOS 4 machine is also good - look for second hand SAM440 machines if you want a cheap intro to AmigaOS 4.
You may also want to look at MorphOS, which isn't AmigaOS but is API and mostly binary compatible so is very close. It runs on old PowerMacs so it's not too expensive to get into, but you need to pay for the OS on top.
Neither AmigaOS4 or MorphOS will run original Amiga software that uses the hardware directly. Software which runs under the OS will often be fine, but you can always ask and we can try it on our AmigaOS4/MorphOS machines.
Also beware this site does tend to be rather anti-OS4, so Utri007's advice is pretty good.