Best motherboard to run win7 ultimate 64 bits?

Excellent. Wow, I have no idea why I initially stuck a Sandy Bridge CPU on that build... Here is a build recommendation that fits those requirements then:

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: Intel Core i3-3220 3.3GHz Dual-Core Processor (£89.94 @ Aria PC)
Motherboard: ASRock Z77 Pro3 ATX LGA1155 Motherboard (£76.30 @ Amazon UK)
Memory: Patriot Intel Extreme Master, Limited Ed 8GB (2 x 4GB) DDR3-1600 Memory (£36.23 @ Amazon UK)
Storage: Seagate Barracuda 500GB 3.5" 7200RPM Internal Hard Drive (£39.56 @ CCL Computers)
Video Card: MSI Radeon HD 7770 GHz Edition 1GB Video Card (£84.54 @ Aria PC)
Case: Xigmatek Asgard II Black ATX Mid Tower Case (£29.62 @ Amazon UK)
Power Supply: XFX ProSeries 450W 80 PLUS Bronze Certified ATX12V / EPS12V Power Supply (£34.99 @ Aria PC)
Optical Drive: LG GH24NS90 DVD/CD Writer (£14.99 @ Novatech)
Total: £406.17
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-03-14 18:11 GMT+0000)

I bumped up the GPU to a 7770 (which will give you a little boost in gaming performance), but that nudged the total price over £400. If you prefer to stay under £400 then you can stick with 2GB 7750 card (Gigabyte GV-R775OC-2GI) from my first parts list. The 7750 should still do OK for your uses.

You should also notice there is no CPU cooler listed. The Intel CPU is a retail boxed option (as opposed to OEM), which means it comes with a CPU cooler made by Intel. Since the i3-3220 CPU is a locked processor, you don't really have the option to overclock. Therefore you don't need to spend the money on an after market cooler. Intel's stock coolers actually work very well and their fans are fairly quiet.

In a nutshell, some of what you have read is true and some of it is false. Here's a bit of a breakdown:

■Yes, Windows 7 64-bit will fit on a 32 GB SSD. You probably won't be able to fit much else though. You would definitely want to try to keep under 20 GB used on that size drive.
■I'll go into the advantages at the end of this post.
■You shouldn't have any issues installing Win7 on the SSD while a mechanical HDD is also connected. You will have to make sure you select the proper drive for the Windows installation though. More on this later as well.
■Yes, BIOS should be set to AHCI mode (not IDE, Legacy, or RAID).

Alright, now the benefits of a SSD are pretty simple. Solid State Drives read and write data much faster than mechanical hard drives. As such, software installs to and loads from, and data files are read from solid state drives much more quickly than they are from mechanical HDDs. This means that, in order to see this benefit in any given program, that program must be installed to the SSD.

In a computer with a 32 GB SSD you will install Windows on the SSD and likely want to move your 'Users' folder and "Program Files" (default program install location) to your mechanical drive, each of which requires a registry change. Under this scenario, you will only have Windows installed on the SSD. All of your other programs will be installed to the HDD. This means your only benefit will be a faster boot time. All of your other programs will have standard mechanical HDD load times. I'm guessing you are looking at a 32 GB SSD costing you roughly $40 or so. So you would then be spending $40 to have your computer boot in 17 seconds instead of taking 45-60 seconds to boot.

I personally will never build a computer like that as the benefit is very minimal for the money you put into it.

The maximum benefit with a solid state drive will be seen when you load your operating system and all your programs onto the SSD and have a mechanical HDD for all your data storage. This usually means you need a minimum of 120 GB capacity in the SSD, but all depends on how much you intend to install on the SSD. Under this scenario you would see the same fast boot times as you would with the 32 GB SSD, but you would also see faster program load times. You would still have to make a minor registry change to have your 'Users' folder get moved to the HDD, but doing this is a fairly simple process. I prefer this configuration because the benefits are much more real and visible. Smaller programs like Internet Explorer literally load instantly. Other programs like MS Office applications are instantaneous as well. I haven't gotten a chance to test load times with more intensive programs like Adobe applications, but I am sure they would load very quickly as well. I have performed this type of setup using a 128 GB Samsung 830 drive without any issues.