Most of the amps people have suggested with the exception of the Atma Spheres are traditional tube amps using iron core transformers. In your price range you will be hard pressed to differentiate other than by feedback and time in market.
Take a look at Linear Tube Audio for both amp and preamp. These are David Burning designs, should run your easy to drive Polks fine in a bedroom, and tubes auto-bias and will last 10-20 years.
Their 10 watt amp is in your budget, is really stronger than 10 watts and will sound better than the traditional options. That plus their MZ2 preamp will make magic together. Plenty of gushing professional and audio show reviews over the last few years. I'm a customer with their bigger amp and preamp, not affiliated.