Some suggestions on changes I would make would be Priest becoming Priest Acolyte, Thief becoming Street Rat, Knight becoming Knight's Squire, and Artisan becoming Artisan's Apprentice.
I can see why Street Rat/Guttersnipe is more of a background than Thief, and why it might be a bit much to allow a 1st level character to have Full-On Knight as his background.
But I don't see how Priest Acolyte and Artisan Apprentice are more background-y than Priest and Artisan. They're just demotions. The standard suggestion should be "my character worked as an artisan before he became an adventurer" or "my character was the priest [of a small country parish] before he became an adventurer," and if people want their character to have never made it past the training stage, then they can decide on that.
Could you have a Wizard Thug, or a Rogue Priest for example?
Of course!
Your Wizard used to be a mean-spirited gang leader. The local band of ne're do wells that used to raid the docks, shake people down at night, fight for their turf, and raid the homes of local noblemen, found it useful to keep a full-blown magic user around. You were right up with the top dog, poised to take his place when the opportunity presented itself, when some very powerful people started to take notice of your little gang wars. Things got too hot, and you skipped town for greener pastures, started raiding dungeons with a group of goody-two-shoes. You never knew philanthropy could be so profitable, but hey, whatever keeps your creature comforts flowing.
You used to be a priest. A nice little parson of a nice little parish. Your people liked you. They prayed to Pelor every night and came to church because of your sermons. But you just couldn't shake your past living on the streets. You'd sneak out at night and raid homes. Shops. You'd pickpocket people on the street just for the hell of it, just for the thrill, just to prove you could still do it. And you couldn't take it. The hypocrisy. The lies. You believed in the gods. You wanted to be a good man. But you couldn't stop.
One day a family came to you crying their eyes out because they'd been evicted from their land, and even the few family heirlooms they could've sold to scrape by had been stolen that night. You'd fenced those heirlooms to a drifter that morning. That was it. You announced that you were resigning from the parish and appointed a successor, a much better man than you. If you couldn't make it good as a priest, then dammit, you were going to help people as the scoundrel you were. You found some "good" people who could use you. Who could pay you. You helped them clear out a few dungeons.
You still send some money back to the parish whenever you can.