While I agree that NAD makes a very good, high value integrated for the money, many of the newer used NAD's do not have phono sections. So check any model your considering carefully.
Also, if you're considering vintage, try and audition it first. Many of these units will be in need of some degree of maintenance and repair such as replacing the caps to bring it back up to factory spec. At the very least, it will need a thorough cleaning such as deoxidizing the pots. If you can do this yourself, great! If your not comfortable with this and need to take it to a shop, then you're probably going to exceed the cost of new.
So if new, consider the Yamaha A-S300 and Onkyo A-9050. Both are within your budget and have phono stages.