If you're planning on getting a GTX560, GTX560 Ti, HD6870/7850/7870, they will have a DVI/HDMI output anyway, so you don't really need integrated graphics.
Anyway I have a few comments to make on what shamsu has said before me.
The i3-2100 is a great chip, however I would recommend you get an i3-2120/2130. It's only a little bit more expensive, and it has a higher base frequency.
I wouldn't recommend overclocking the i3's at all...As the multipliers are completely locked, and base clock overclocking is very risky.
Now onto your question about different chipsets.
H67 - Has the ability to use the Integrated HD3000 Graphics on your Intel Core CPU's, but has NO overclocking ability.
P67 - Gives you the ability to overclock your CPU but absolutely NO ability to use the Integrated Intel Graphics.
Z68 - Gives you the ability to Overclock AND use the Integrated Intel Graphics. Basically Z68 has all the features the other chipsets have respectively. And a few features special to the Z68 chipset, such as Intel Smart Response technology (or was it called Rapid Storage Technology?).
Now about i3-21xx vs i5-2500k, there is a pretty big gap in performance due to the i3 being a dual core (with hyperthreading), and the i5 being a TRUE quad core CPU.
Now as you said you don't plan on overclocking, what is your budget? Maybe you can squeeze in an i5-2400 in your rig. The 2400 has NO overclocking capabilities as it's multiplier is LOCKED, and it's an i5, meaning it has 4 real cores instead of two hyperthreaded ones.
Also about your GPU, I would highly suggest getting a Radeon HD6870 or GTX560 Ti. They will offer more performance for just a little more cost.
TL;DR - I would suggest getting a beefier GPU, such as a HD6870 or GTX560 Ti, maybe a Radeon HD7850 if your budget allows it. The i3 2100 do fine, but I suggest a i3 2120/2130. Motherboard is up to you, I would personally get a Z68 board for upgrade purposes in the future, but an H67 motherboard may do fine for your needs.