I've had the pleasure of trying out all the headphones you mentioned and what i'd have to say is, go to your local headphone dealer and try all of them both amped and unamped... sound is definitive so what i may find as bassy might be not even close to bassy by your standards. but i'll give u my views on them just as reference i guess
now the srh440 and hd558 are more neutral with no emphasis on trebles, mids or bass... unamped, they don't sound very special really. Drive them well, however, and you'll get your money's worth and more.. personally the bass on the 440, to me, were recessed. the bass(guitar) on most of the rock songs i tried, ie led zeppelin's whole lotta love, were less punchy. Its there, don't get me wrong, and the bass do sound good but thats where they stand. Very good, control-ed bass that's clear and dosen't distort. Perfect for monitoring purposes where u want clean and clear sounds that don't over power the other frequencies. Not so good for bass heads, gamers and certain music where u want that boomy punchy feel from the bass,ie techno, rap. This is when ur amped. The 558 fairs slightly better on the low ends but not by much. The treble and mids on both are where they should be. Definitive but not overwhelming, bright or pitchy which ever u call it. The sonic values on these two are more balanced and neutral so i'd suggest you stay away from them unless u want clearity, revealing, "speciality" headphones.
Now the srh djs are pretty much what the 440 and 558 are but they're more equipped on the bass side. Again you get clearity and great sonic values but now they're more coloured towards the low ends. Not nesscessarily basshead material but they're more punchy and robust. Think of the bass on the 440 and 558 as a glass of mocha while the srh djs as a shot of expresso. They've got more omph and feel.
all the shures are closed back, noise isolating headphones but the difference is that the 440 is circumaural while the djs are supra aural. Go wiki those up if u don't know what it means. The 558 are circumaural open backs so there'll be noise leakage... lots of it... All the shures have low impedence so you can drive them from ur ipod or phone. U don't get the fullest sound though. thats where u need amplification...
Ur better off with sth lower end though because you'll start to notice very small differences once you go over the 140usd mark... like how crappy mp3s can sound sometimes. i'd reconmend the sennheiser hd448. they're small, light, very good sound for the price, closed back, noise isolating, bassy and relatively cheap circumaural headphones. A good starting point for an all rounded headphone that meets some, if not, all of ur needs. Most of the people who go for the hd555 and above, shure srh440 and above know what sound is and what kinds they like. they're more mid range-ish audiophiles. you're starting out so i'd suggest starting small then working your way up. u don't wanna end biting off more then you can chew.
so go and try them out. what i like and think dosen't mean they'll apply 100% to you. lol