I picked up a Rem 700 ADL in 270win a few years back for 450.00. (intended project rifle) Yeah, the bluing was rubbed quite a bit, the stock was surprisingly nice but it lacked sights. Bases and rings for that are easy to obtain and inexpensive, and a simple Weaver K series can be had for ~100.00... when funds later allow, the scope can be upgraded to something clearer though they are a decent old optic.
450.00
+100.00
+ 70.00 new rings/bases (or make do with an old and inexpensive Weaver style)
could = between 570 and 630 and exceed your requirements. But if time is an issue, you'll likely end up having to pay more. I was only looking for a future build platform when I found the rifle.