What motherboard for I3.

Why would you buy a LGA 1156 CPU if you don't already have a LGA 1156 motherboard? It just doesn't make any sense.

The much smarter choice is to buy an i3 2100/20 (or even an i3 3220), and get a new 7 series LGA 1155 motherboard.

Good LGA 1156 boards are getting hard to find these days, but good LGA 1155 boards are out there in abundance.

Im going to buy the cpu with the motherboard.And I dont want to spent too much money.

Well, it's not going to be easy to find a LGA 1156 board worth buying.

i3 2120: Intel Core i3-2120 Sandy Bridge 3.3GHz LGA 1155 65W Dual-Core Desktop Processor Intel HD Graphics 2000 BX80623I32120 $124.99

H77 Motherboard: ASRock H77 Pro4/MVP LGA 1155 Intel H77 HDMI SATA 6Gb/s USB 3.0 ATX Intel Motherboard $79.99

OR, B75 MATX Motherboard: ASRock B75M-GL LGA 1155 Intel B75 SATA 6Gb/s USB 3.0 Micro ATX Intel Motherboard $59.99

IF you dead set on that i3 550, this is pretty much your only option (at least from Newegg, and it's NOT cheap): BIOSTAR T5 XE LGA 1156 Intel P55 ATX Intel Motherboard $134.99

Unless you're getting that i3 550 for next to nothing, it doesn't make any sense to go in that direction. The newer stuff is the way to go.

Pick up the Intel® Core i3-2120 and a H61 chipset based board. This will give you better performance at $200 or less.