I can easily obtain a Windows Server key, since I have DreamSpark access courtesy of my college. Which Server OS would you recommend, though?
I already have Server 2003 on one of my towers, but it doesn't even have 100GB free of hard drive space, and I already use it for other functions as well.
Use whichever version you are most comfortable with. (Personally I'd go with 2012R2)
Is your 2k3 box a DHCP server?
Edit your DHCP server option 66. It's called the Boot Server Host Name. Add your new server host name there. (Make sure you are able to resolve the host name of the new machine, might have to add a DNS entry on your server if you are not in a domain.)
Once you have WDS installed, you need the Boot.wim file from the Windows Installation Media (DVD or ISO). This can be from Server ISO if you want, it honestly doesn't matter. What does matter is using the latest version of the Windows NT kernel PE environment. You can not deploy a Windows version with an older PE. For example, you can not deploy a 6.3 install from 6.2 WinPE, however, you can deploy a 6.2 install from 6.3 WinPE.
Open the WDS console, and import the Boot image by right clicking on the Boot Images folder on the left and select Add Boot Image.
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Once you have the boot image imported, on the right side, right click the boot image you imported and select create capture image.
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Once the two images have been configured in WDS, it's time to capture your image. Boot using PXE on the computer you are wanting to capture from, and select the Capture image from the list of available boot images.
Run though the wizard and you will have a captured image. Once the image is captured, you can either manually copy the image file to the WDS server, or select the option to automatically copy the image file to the server during the capture wizard.
Note, The capture wizard will only work if you have run Sysprep on the installation you want to copy. I would recommend running Sysprep in audit mode and deleting any user account you created during the initial install of Windows. Also install any programs and windows updates at this time. This will make it easier once you have deployed Windows to another machine.
I left things kind of vague as half the fun of doing IT things is figuring it out as you go along, but if you get stuck or have questions, I will happily answer them. I can create a step by step guide with screenshots if you need them.