hello,
the only thing i'd work on right out of the box is the trigger pull weight. i'd shoot the rifle, maybe going through 100 rounds, before even thinking about free-floating the barrel. i'd re-crown it, if needed, before free-floating it. (if needed.......).
i just don't believe that free-floating is the end-all to everybody's accuracy quest. and many times Remington has proved, with pressure bedding, that free-floating isn't worth it. if the barrel has been properly stress relieved then it may not change point of impact when warming up. at least, it won't change anywhere near what you sometimes read about rifles that probably weren't stress relieved properly.
take care,
ss'