Minimum requirement are often not a very good indication for how well a game will run today. You have also to remember that since that time your Windows system might have been updating several parts including DirectX which is the base for this game to run. Then your drivers for video card might also be less efficient as those drivers tend to include newer video card and less support for those older generation of GPU even if you use an older version of drivers a year or two after your video card came out.
I would suggest that for your new build will make use of an Intel i5 which is a four core CPU as those CPU will work better for older games like Oblivion and for Skyrim. AMDs option for CPU will also work, but they are known for not being as good in IPC (Instruction per clock) for each core and even an 8 core (FX 8350) will be on par with an four core CPU from Intel (i5 4670K) in most games except for Skyrim (and I will deduce that it is the same for older game like Oblivion). In this case older games like Oblivion or Skyrim have been designed for dual core and will not make use of threading that much, so higher IPC will be better. You can confirm this by taking a look for benchmarks here on THG for Skyrim and how FX vs i5 perform.
There is also a RAM limit in how much Skyrim will make use of more RAM then 4 GB. More RAM will be good to have in general and will have its place in that game too with mods and so on, but it is not necessary to go over board just to run this game. (Search for Skyrim and RAM limit - there mods and there are suggestion how to make use of more RAM).
Depending on how high resolution (especially for textures and visual mods) you plan to use, there will probably be good to have around 2 GB Video RAM on a discrete video card or more.
If you are short on money, then you could first make use of the integrated GPU on i5 4670K (Intel HD 4600) to run Oblivion and later add a discrete video card (but turn off the iGPU in BIOS to avoid conflict with drivers for video).
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I use Skyrim as a reference as it is the latest game after Oblivion and it is easier to find benchmarks both for CPU and GPU which is on today's hardware. You might find some YouTube video for Oblivion on modern hardware which could give you an idea of how it will perform on different combination between GPU and CPU.