Which lga1155 motherboards support integrated graphics

Good on you!

All 1155 MB’s will have this statement:

Onboard Video Chipset: Supported only by CPU with integrated graphics.

That said, your Pentium g860 is advertised as having Intel HG graphics. ($75)
However, that will get you a monitor output and will be good enough to serf and play a few movies off netflicks.

Thats it.

Any serious gamer needs a serious graphics card. Put the money your saving on the Pentium (which is fine for a low budget system- don’t get bullied into spending $200+ on an i5 by the snobs on the board) into a card that can really do something, like this one:

http://www.newegg.com/Product/Product.aspx?Item=N82E168... ($178)

Since you are getting a 32nm chip you will not be able to get a Z series board as they require a 22nm chip. I’d recommend an H77 series like this one:
http://www.newegg.com/Product/Product.aspx?Item=N82E168... ($79)

Get at least 4gb of PC3 12800
http://www.newegg.com/Product/Product.aspx?Item=N82E168... ($19)

Get a single rail power supply from a reputable company. (Antec, Corsair, Thermaltake, CM, Seasonic, Rosewill) 80+ bronze minimum
http://www.newegg.com/Product/Product.aspx?Item=N82E168... ($49)
Get a smaller (160GB) 7200 speed hard drive for your OS
http://www.newegg.com/Product/Product.aspx?Item=N82E168... ($20)
And maybe a separate drive for your storage. If you have some money left over an SSD will vastly improve your experience.

My recs give you $420 spent, which leave some over for an OS and a case.

The only chipset for socket 1155 that didnt support IGP (Integrated Graphics on Processor) was the P67 chipset. However there were some Z68 boards that didnt support the IGP. To my knowledge all of the "7" series boards for socket 1155 support the IGP but you might want to check to make sure. Simply check to see if the board lists any graphics ports (i.e. DVI, EGA, HDMI or Display) and if it has any of them then the board supports the IGP.