Sadly your nice modern system does limmit your options a bit - SATA being the main factor.
At this point I guess I should come clean & say of the options Amithlon is my preferred setup...
...having said that:
-Amithlon: Does support *some* SATA, not yours sadly. The main problem for you is your nice dual-core intel CPU & GFX card - If any can prove me wrong I'd be happy to hear but Amithlon won't run on multi-core CPU's. (slight lie here)
-X-Amiga: A great alternate to the above if you're after booting stright to AmigaOS. No SATA at the mo' but the author is working on it.
-KX-Light: (Cloanto's X-Amiga) Will probably work but isn't as 'good' as X-Amiga, is a bugger to HD-Install & the docs are non-existant. (another slight lie)
-AmigaXL: (part of the Amithlon package) May work on your system if QNX (the underlaying OS) supports it.
-AROS: It's gonna be great! But at this stage still a swine to install. Especially if you already have data you don't want to loose. (I didn't know about the lack of SATA support)
-OS4: I agree.
-WinUAE: Wonderful, but a problem if you don't want to boot 'doze first. (You can replace the explorer.exe 'shell' with winuae.exe for a more 'authentic' experience but there are issues...)
-E-UAE+Linux: Currently your best bet given what you're after & your hardware. (TBH: I'm not a Linux fan but if you are...)
As you've discovered getting hard to find & d*mn expensive.
FWIW: Nothing beats 'the real thing' but if it's been a while a max'd out miggy comes nowhere near any of the above in performance / convenience...
...run a good emulator for a while and when / if you set up a real one you may be a tad unhappy.