I'm probably throwing way too much at you since you're just getting into this, but for the benefit of other people reading this thread and keeping your expectations in check, here are my thoughts.
I'm interested in including more newer games into my MAME cabinet(such as Soul Calibur III). So, which type of PC do you recommend I purchase?
The only emulator that supports Soul Calibur III is PCSX2 (Playstation 2 emulator).
To run that game on that emulator, you'd need an expensive bleeding edge top of the line gaming PC.
You'd be better off putting a real playstation 2 in the cab if that game is important to you.
Most people only play classic 80's games and 2D fighters from the 90's on their cabs, so that's what the specs mentioned so far are good for.
But they aren't going to cut it when it comes to running 3D games and emulators for newer arcade games.
If you want to play the newest games that are emulated, you'll have to use emulators other than MAME. (Demul, Supermodel, Dolphin, etc)
On processor speed (most important spec):
Tekken 3 in MAME for an example:
When I had a 2.8Ghz Athlon X2, even with a lot of tweaking I still had some sound skips.
With a 3.2Ghz Athlon X2, the sound skips went away but there are still other 3D games like Time Crisis that it struggles with.
For emulators that run newer games that MAME can't, this is pretty much a bare minimum.
The current best option seems to be the Intel i5 2600k, but it ain't cheap.
It's a huge overkill for most of what people play in MAME, but you said you wanted to play newer games.
On # of cores:
On my driving cab, moving to a triple core processor made a bigger difference than I was expecting. Last time I checked, MAME only utilizes 2 cores (this will change someday), but the extra cores help out with all the windows stuff running in the background. Other emulators will utilize the extra cores.
On the Video card:
A basic video card will work fine for MAME. Other emulators that run newer 3D games (Demul, Supermodel, Dolphin) heavily utilize the video card. I'm too far behind on the current crop of cards to recommend one. The newest version of Demul is useless without Directx11, so make sure you get a Directx11 card if playing the newest games possible is important to you. There was an arcade system called Taito Type X which was just a regular windows pc in a cab. These games have been cracked and will run on a regular PC (no emulator required), but people have reported problems getting them to work with ATI video cards.
These other emulators aren't anywhere near as easy to set up and use as MAME. You may just want to accept that your cabinet will be limited to 80's & 90's games, but the computer will cost a LOT less and be a LOT easier to set up. It can be a case of diminishing returns where you are spending a fortune and spending a lot more time just to get two or three more games playable.
If you buy an older used computer, try to get one with a 64bit operating system as that results in a pretty big speed boost for MAME.