You do not need a device, and can archive when it's set to iOS Device. The best bet is to test on as many devices as you can, and archive when it's plugged in. Although when it says iOS Device, you can archive. The reason it's grayed out is probably an error in your provisioning profile or certificate. You may want to look under Organizer under profiles or under your build settings.
You need a development certificate for testing locally and distribution certificate for submission to the app store. You need to create a request in keychain then submit it using iTunes Connect, and then download the proper provisioning profiles and certs, and install it in XCode Organizer.
Best bet is to purchase a cheap device like an iPod Touch or iPhone, that can test most of your capabilities (iPod doesn't have most capabilities). You can compile for iPad with iPod or iPhone. So you just need an iOS device that can support your version 4.3+ or 5,6,7.
My previous answer was not correct, but this one is. Trausti was actually correct.
与恶龙缠斗过久,自身亦成为恶龙;凝视深渊过久,深渊将回以凝视…