If you are looking at the 16GB Nexus 5, the Google Play Store sells it for ~$350, so it is $50 cheaper than it is from T-Mobile and it is the same phone.
For your phone number, you should port your phone number over while you are activating your plan online. Because this plan is for new customers only, you want to make sure that you do this process online all at one time.
For your contacts, there are many ways to get them over to your new phone. Since you have an iPhone now, I would recommend syncing your contacts to something like GMail or Outlook. That way, you can sign in to that account on your Nexus 5, and your contacts will automatically appear on your phone. If you prefer not to sync your contacts to the cloud, carrier stores can usually do this transfer for you. You would do this after you activate your new SIM card and plan.