That's actually not an easy list to answer in point form, there's too many "if's/ands/buts", so I'll give a brief rundown of Amiga hardware and hopefully you'll get the information you need.
The following is written around what's regarded as "classic" amiga's (the one's made by commodore (a500/a600/a1000/a2000/a3000/a4000/etc.). The machine equipped with motorola 680x0 cpu's. There's technically probably a few inaccuracies(like disregarding os4), but for the original posters questions its the info he wants (hopefully)
Firstly Amiga computers are based around 3 chipset models, ocs, ecs, and aga. OCS and ECS are very similar with the same 4096 color palette and onscreen color restrictions remaining the same. The main 2 differences are that ECS can have 2 meg chipram (the ram amigas use for gfx and sound), whereas ocs can only address one, and ecs has an additional screen resolution. AGA adds further resolutions, has 16.777216 million colors, and can display more colors onscreen that ocs/ecs, as well as other assorted extras.
The other thing that's probably most important when it comes to amiga hardware is the OS/kickstart rom version. With Amiga's as well as installing the operating system on to a harddrive (or floppies), there's what's known as the kickstart roms, which are physical chips that slot into the motherboard. These chips, as well as dealing with low level hardware also contain essentially what is the "core" of the amiga operating system. These chips dictate to the same degree as the chipsets what software can and cant be used/backwards compatibility, and so on. As such it's entirely possible to run the latest version of amiga os on even the oldest amiga model if its Kickstart has been upgraded.
In addition to this its also possible to upgrade things like ram and cpu to varying degrees depending on the amiga model in use. The "box" amigas can also take additional cards like graphics or sound cards, which will speed up use and/or give a better quality. On top of this there's also lots of upgrades to add things like pci busboards (ergo pci graphics/sound/etc cards) and usb connections.
One final thing that's probably worth mentioning is that a good portion of the amigas software library (games that run from floppy disks mainly) are reliant on a particular custom chipset. OCS/ECS isnt often a problem in this regard, but there's a not unnoticable portion of games written for ocs/ecs that wont work on an AGA machine. To get around this there's WHDLoad, a program written both to make games installable to harddrive (games that "lock out" the OS and use the chipset directly typically wont install to harddrive) and to help with compatibility. AGA games require an AGA machine though, WHDload or not. Software that is written to use the OS will most of the time install to harddrive easily and work on most amiga models (given enough ram and fast enough cpu).
