I apologize for the delay in responding, and thank you for posting, Tiziano. Your live sound experience will help a lot on set. Today in that price range, compact recorders from Zoom, Tascam and Sound Devices (MixPre series) are popular with boom operators and sound mixers.
Look for good preamps, 32-bit float recording (which makes clipping much less likely), timecode if you need it, and XLR inputs. Our Sound forum is a great place to compare.