You shouldn't run into BIOS problems - it's built into the motherboard and really can't be messed up by swapping out components. I think the problem you're referring to is when you replace a motherboard WITHOUT doing a clean install of Windows. If you do that, you'll likely have all kinds of problems from driver conflicts, because the drivers from the old motherboard will still be there on the hard drive, and it's pretty close to impossible to untangle.
Anyway, if you have mobo, CPU and RAM all at once, you're basically replacing the whole guts of the machine except the hard drive, video card (if any) and power supply. A lot of Pentium 4 machines use the old IDE/PATA type hard drives, which uses a completely different connector from the current SATA standard ... but your new motherboard looks like it's one of the ones that has both types of connectors, so you're in business. Video card may be another matter depending on what kind you have, but at least this new board has onboard video so you'll be able to get display one way or another.
To install Windows, yes, start the PC with the disc in - but before it boots, you'll probably have to hit F2 or del or whatever key triggers the BIOS. There should be a setting in the BIOS for "Boot order" or "Boot priority" or something like that, which tells the machine where to try first to boot from. Normally the hard drive is the first priority on this list, so you'll have to change the setting so your CD/DVD drive is first and hard drive is second. Then it will read the DVD first; if you don't do this, it will go straight to booting Windows from the hard drive and read the disc later.
By the way - in case it wasn't clear - install Windows 7 AFTER assembling the new machine. You probably knew this, but I have seen cases where someone made replacements like this but installed Windows BEFORE, when the old motherboard was still in place. That's just going to cause you to have to reinstall Windows again.