Move my OS to my new HDD

Well, it depends on what you got.

If it's a desktop you can install the new drive and then clone the old drive to the new drive (using disk imaging software) and be done with it.

If it is a laptop you can create an image of your entire drive (using disk imaging software) to you external drive (the image will be approx. one half the size of all the data on both partitions at normal compression) and then restore the image to your new drive.

You can re-size the partitions afterward using Windows Disk Management, or a third party program like Partition Wizard.

If you have the room for a second drive as you would see on a desktop you can create a full image from the 250gb to temporarily store on the external 1tb drive provided the image isn't too large and see it restore onto the new 500gb. I wouldn't recommend resizing the C volume once restored however.

If you have no plans to see a fresh install of Windows on the new drive the first thing to take care of would be running the System File Checker tool as well as scheduling a run of the Disk Check tool to make sure everything as far as any drive errors or problems with system files is taken care of before creating the image. You want everything to be in the best possible working order before seeing the hardware change.

For creating the system image you have two options one being the built in backup tool or the use of a 3rd party program like free version of Acronis provided by both Western Digital and Seagate(rebranded to Disk Wizard) which will compress images down much further then seen with the Windows option. That may even allow you to grab a pair of images in case of one not going so well while these are usually quite reliable.

Are both drives still connected?
You may need to temporarily disconnect the old drive.

If the old drive was still plugged in that would see 8 start up ifrom still having the original installation intact. This is why creating a full system image and restoring that to the new drive would like have seen immediate results.

You may still see have to see a clean install however where a backup made with the Windows Easy Transfer tool for files and settings restored onto the clean install once you have all the same programs back on again. How to use Windows Easy Transfer to transfer files and settings in Windows 8

Cloning drives usually works best when both drives are identical not seeing different sizes or by different manufacturers.