You can shrink the Win 8 partition a lot and then Mint 14 can automatically install into free space with the "Install alongside Windows / other OS" option. But you need to make sure that if your Windows is booting in UEFI mode, then the Mint DVD needs to be booted in UEFI mode too (not in legacy mode). You may also need to disable UEFI Secure Boot in your BIOS.
If you delete the Windows partition you may not be able to "install alongside other OS" since there's probably no other OS anymore. Some recovery partitions, however, (those on HP laptops for example) are seen as an operating system too, so those allow using the "install alongside" option for automatic installation into the free space, even if there is no Windows. I do not know how that works with Lenovo's recovery partitions.
@ Pierre: PAE is enabled by default in Mint 14 32-bit so RAM is no longer an issue. Anyway, you can use 64-bit edition on your computer and you have plenty of RAM, so 64 is preferred indeed.
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