Create a Clone of System HD
I would do the following to avoid hassles.


Download the installer I want from a running OS and use it to make an official USB installer drive.
Make a Time Machine backup of the 250 GB drive to the drive you will use to back up the Mac once it's running from the 500 GB drive. If you plan on no backups, beg/borrow/buy a drive at least 500 GB to use temporarily.
Boot to the installer drive to test that it COULD install to the 250 or the 500 GB drive, but don't install yet.
Power off the Mac and put the 500 GB drive inside.
Boot to the installer with no other external drives connected. Use Disk Utility from the installer to wipe the 500 GB drive and repartition it as OS X Extended.
Once you install to the internal 500 drive, connect the Time Machine drive to restore the backup you made earlier.
Keep the 250 drive safe for a while. You can always connect it to recover files if you discover Time Machine skipped some data or files you need.


I know Carbon Copy Cloner has a way to make a clone bootable, but I don't use that tool, so perhaps my mentioning it will get someone to step forward with that experience.

Also, cloning the drive will carry forward disk errors so you really don't want to do that. Cloning also bypasses the new default settings. Why run in old crusty settings when you can choose what customizations you miss when they occur to you and make use of the new features fully.

There are a few cases where I clone a setup, but the drawbacks almost always make me wish I had started clean so I save little time if any by cloning these days.