Do you wish for a board that supports SATA 3.0 or USB 3.0?
Do you wish for a DVI port or is VGA (D-Sub) port enough for your needs?
Do you require an IDE drive connection or will SATA be all you need? (boards with IDE support seem to be expensive)
Will you be needing Micro-ATX or ATX form factor?
The P67 chipset does not support on-board graphics.
For on-board graphics, H61, H67 or Z68 chipsets are what you should look for. Since you are looking for a budget board, you will probably want to go with the H61 chipset.
Please don't ask us to pick out a board. All we can do is help guide you in the direction you want to go. We can give a few suggestions but ultimately you must be the one to choose.