The right choice for you if you're a new or returning user will depend greatly on what you want to do, and what your motivations are.
The following are the most viable alternatives for someone reasonably new:
AmigaOS4.1 runs on new hardware from ACube - the SAM series of boards, that are available from an number of Amiga retailers or direct from ACube.
It is also set to run on the forthcoming AmigaOne X1000 from A-Eon, and the new SAM 460ex from Acube.
Out of production machines that can run AmigaOS 4.1 includes AmigaOne-SE, AmigaOne-XE, Micro-AmigaOne, Pegasos II.
If you want to seriously use AmigaOS4.1 as a new user, whichever of the SAMs or X1000 will be your best bets.
This is perhaps the most pleasing retro-gaming alternative.
You can pick up classic Amiga models on E-Bay or refurbished or “old new stock” (e.g. unused but old hardware) from a number of vendors (TODO: Links and more details). If you're a returning ex-Amiga user that want a classic Amiga, you have your pick of whichever models you preferred. But you may want to take a look at an emulator first - the shock of how basic the OCS/ECS machines seem today might drive you to look for expanded later model “big box” machines like the A4000, that can be upgraded with things like graphics cards.
If your goal is to play the old games, however, and you insist on a classic,an A500 or A1200 is likely to be the best alternatives.
The other alternative is to buy (or build, if you're good with a soldering iron and have copious amounts of spare time) a Minimig, which reimplements a somewhat expanded A500, sort of. You also need Kickstart ROMs, which you can get by buying AmigaForever.
Which version of AmigaOS to run on these machines depends on your goals and the hardware. If you mainly want to play games, newer versions of AmigaOS may be counterproductive due to compatibility issues. AmigaOS versions up to 4.0 works on classics (A1200, A2000, A3000, A4000), but 4.0 requires a PowerPC expansion board. For unexpanded classic Amigas, the most recent option is AmigaOS 3.9, but many classic users also use upgraded/customized versions of 3.1 and 3.5 as well, as the changes after 3.5 consists largely of including third party extensions.
Two new options are on the way for classic hardware:
As of writing (May 2010), both of these boards are still in development, though a production batch of the FPGA Arcade board may be available “soon” (e.g. PCBs have been manufactured but not yet populated).
If all you want to do is play around a bit, and play some games now and again, this is likely the best alternative. It is also a good alternative if you want to work seriously with “classic” AmigaOS or want a genuine AmigaOS setup but without paying the cost of a PowerPC system or AmigaOS 4.x
Get AmigaForever. You need a source of kickstart ROMs, and these are provided on AmigaForever (you can get your own images by extracting them from a real Amiga as well, if you prefer, but the AmigaForever route is simpler). If you're a Windows user that gives you a pretty nice setup out of the box. If you're on Linux or OS/X it's a little trickier. You can also set up WinUAE (best alternative on Windows), E-UAE or UAE (on Linux and OS/X)
If you want an AmigaOS like operating system on cheap commodity hardware, AROS is worth a look
AROS is an effort to re-implement AmigaOS 3.1 plus some extensions and improvements from newer versions. AROS can run on bare x86 hardware if you pay careful attention to what you can find drivers for. AROS versions for PPC and 68k are also in various stages of completion. Alternatively you can run AROS “hosted” under Linux on any platform Linux has drivers for.
Because it runs on x86 it is probably the most cost-effective solution in terms of performance. With upcoming tighter E-UAE integration, it is also becoming easier to take advantage of classic AmigaOS software on AROS (you can run most of them in E-UAE isolated, but the integration work will mean the applications will seem more like “normal” AROS applications for you as a user)
Like AROS, if you want an AmigaOS like operating system on cheap commodity hardware, MorphOS is worth a look.
MorphOS runs on various PPC based hardware platforms. Currently supported are Pegasos I, Pegasos II, Efika, Apple Mac mini, eMac and PowerMac models. Apple PowerBooks are supported in MorphOS 3.
MorphOS runs system friendly AmigaOS software (up to 3.x version) and its own software developed for MorphOS.
It is perhaps the most user friendly and cost effective platform to run Amiga software on modern hardware. It comes with modern 3D drivers, MUI 4 and CyberGraphX software.