I think the best deal on headphones is the AGK K240 that Sweetwater currently has for $99. That is close to half price. One thing, the K240 are "open" headphones and don't block exterior sound as well as closed type. But closed headphone for the same sound quality cost
at least double, maybe more. For your target price you will not do better than the K240.
Monitors... The best I've found so far are a pair of floor standing speakers made for Stereo and/or front channel home theator use. This class fo speaker is about 36 to 40 inches tall but very narrow, maybe 10 to 8 inches wide. Polk makes some called the R50 and also M60 and m70 that are a good value when they go on sale. Prices are from $50 to $110 each. If you can't wait for a twice a year sale the R50 are a here
R50 Polk seems to make both M and R versions of 50, 60 an 70 (m50, r50, m70,....) Newegg.com. Fry's and Amazon move the prices on these up and down over a factor of two. But the above deal is prety good.
You would need am amplifier. Any 100 WPC stereo reciever would do but I use an AudioSouser amp-100 I bought at Amazon for $99. In a larger room I'd use two of those each one set to "mono". With two of these amps and two speakers you are at about $425 and the sound will be better than any studio monitor I've found.
OK, if you must have self powers studio monitors look for a pair with 8 inch bass drivers from KRK, Yamaha, Mackie or any of the other first tier brands
Not matter what sound system you use the room itself matters a lot. If you ever buy a measurment microphone and some software you will be amassed atthe effect of simple things like moving a speaker three feet from a wall make. Ppeople spend all kinds of time an energey thinging about which brand of speaker to buy and then zero on how the speakers will be placed, aimed and other acustic treatments to the room. If you experiment you find all this matters a lot more than the brand of speaker
The physically larger speakers that I like now, I think "work" because they tend to fill the rooom with sound rather then the small monitor that beam the sound directly at you. The "fill the room" is more like what an acoustic piano does. Monitors are designed for "mixing" and are "accurate" They are best used in conjunction with those K240 studio headphones if you do any recording. I have a pair of monitors and they sound, well like monitors. But I use some other full size speakers in the living rooom for lightening to music.