Do they transfer everything from an old iPhone to a new one at the store?

This Thursday I'm going to get an upgrade. I have an iPhone 4 and I'm not sure which one I'll be upgrading to yet. But I was wondering if they transfer everything from your old iPhone to your new one (pictures, contacts, texts, apps.) It's really important that I get all my contacts into my new phone imediately, and although photos are important to, they're not absolutely mandatory. Before I go to the store I'll probabky transfer my photos onto my computer just in case.

Transfer your data onto your computer, as the data won't be moved by the store. Then, when you get the phone, transfer the data to it.

Call up the store ahead of time to make sure that they can do what you need done. I have found that depending on the Apple Store, some are able to do things that other stores can't, because they are short staffed, or only do certain types of thing by appointment vs walk ins.

Yes but you can also do it yourself, just click backup on itunes then when you setup the new you choose to copy from backup.

You could do that yourself if need be through iTunes which is what they would more than likely be using anyway. Contacts shouldn't be a problem. May take a while to get the backup started depending on how often you do so on your own.

I work for a major carrier. Some stores are equipped with a device which can transfer contacts, photos, and videos from one phone to another. Privacy laws may, depending on where you live, not allow them to store, even temporarily, your data on their systems, so these devices transfer directly from phone to phone. Call ahead as others have said to see if they have this capability.
Alternatively, to get a more complete transfer, use Itunes to do a backup of the old phone, and restore it onto the new phone. This covers virtually everything on the phone.

I think you can make a backup file for your iPhone 4 on your iTunes and after your get an iPhone 6 or 6 plus. When you set up the new iPhone, you can restore your new iPhone with the backup file via iTunes. So I think everything on your old iPhone 4 will be on the new one.