Monitors or floor standers... whew! this continues as an ongoing debate... for me too.
it is easy enough to see the same floor space is used either way floors or monitors on stands... the added need is for the sub (s), if mons are used.
Stan's suggestions are very likely mighty good ones, as he has a lot of exp here. LSA also makes speakers. Talking to the designer some time back he cleared up a few things for me on this very subject, and you might want to take a look at them as a tact towards keeping/gaining synergy in your outfit.
your room is going to dictate your bass issues nearly as mmuch as will the speakers you put in it. both have to work together. Personally, in that size room, (mine is close to yours but just a bit larger), and I do feel the need for a sub... most of the time.
Active subs also reduce the needs for greater power and bigger bass drivers in floorstanders. Given all I've seen on subs here and elsewhere, having two looks like the way to go.
$3K ought to get you some nice near full range FS. Remember, mons will also need stands... and very likely one sub.
Good lick