A related question is what kind of hardware is the target? My old PC is similar to today's PS4 Pro, and it can run the old game without a hitch. When the old game was written, however, back in 2004, my hardware would have been off the charts.
(In 1980, I used to buy computer systems for Motorola, and just for fun, I calculated what my home PC would cost back in 1980. Each 300mb disk back then cost $15,000, and my 3 TB disk today would be 9,000 of those! Disk cost alone would be $135 MILLION!!)
Anyway, the graphics capabilities of the target hardware will tend to set the budget for the graphics. But we know in 2-5 years, the hardware will improve, probably dramatically.
So the question really is: what would you trade-off? Models and environment? Graphics effects? And *what hardware is the target*?
After looking at the user specs for the login test, I would say that this is the minimum to play;
1st gen i5 dual core CPU with a dedicated graphics card on the lines of a GTS450 or a Radeon 5750. These are entry level numbers. This requires turning graphics to minimum. Using built on Intel graphics would likely need a 6th generation quad core CPU, once again with settings at minimum. Intel onboard graphics use a lot of software emulators, which puts a lot of stress on the CPU. A dedicated video card would be just about required with an Intel CPU.
AMD has a huge lead with onboard graphics. Estimating based on similar games with similar Intel spec requirements, a 2nd or 3rd gen A8 quad core would run the game at above minimum. The onboard video for any Ryzen 2nd gen CPU should play the game very well, although probably not at max settings.
If I was going to recommend a value system that should play the game at or near maximum graphic settings with a good FPS, I would recommend the following;
INTEL BASED: a 6th gen i5 quad core or newer/ faster, teamed with either an RX470 GPU or faster (such as Vega series) or An Nvidia GTX1050Ti or better. The 1050Ti performs at about the same level as a GTX 970.
AMD based: Ryzen R5 - 1600 or faster teamed with an RX 470 or faster, or a Vega 56 or faster.
As far as cost effective system, I would get a Ryzen 5 - 2600X and just use that without a dedicated card. The built on Vega 10 graphics should play the game just fine, although not at max. Then in July, when AMD releases their NAVI GPUs, I would get one of those that is priced about $250. This setup should easily play SoH at max graphics. A complete system based on these parts, including the GPU and a copy of Win10 but excluding a monitor (why buy a monitor when you can just use your TV and get a much larger view?), with 16GB of RAM, and a 512GB SSD should price out well under $1000. You could probably get a Ryzen 7 2700 and still stay well under a grand. That one is 8 core/ 16 thread and uses slightly superior built on graphics, Vega 11.
Or, if you are not in a hurry, AMD is releasing their 3rd gen Ryzen CPUs in July. One of those, with a NAVI video card, should rock the socks off of SoH.