Good advice from Falkyrn.
On really important stuff such as photos & other things like music, I`ll always copy & paste.
Yes its long winded, yes its boring, but you can then click on a sample of the files afterwards & test them, very boring & not the most exciting thing to do on a Weekend off, but if its important to you its worth the effort.
Back-up software is good on the whole, but it can go wrong even when you`ve "Verified the back-up", you`ll only know theres a problem when you come to resurect the back-up & it doesn`t work.
One thing a lot of people forget to back up is emails, yes they are only emails, most folks use an email client & ALL emails are downloaded to your PC & then deleted from the e-mail server...its always worth while backing up emails or open a Googlemail account & forwarding all emails to that as a back up, without deleting the original.. You can use G-Mail as a virtual HDD as well, it can be handy for small transfers of data to trusted friends....A couple of 100s of Mb/a few Gbs of photos can be transfered by this method...
As you have a New PC arriving there isn`t such a major problem as upgrading you Original PC, you can keep the original PC running until you are happy that you haven`t forgotten something...believe me thats easily done.....
Remember don`t rush, have patience & Tea or a Beer sometimes works well.