Ok. Humbuckers are not "rough." All types of pickups are capable of sounding sweet or gritty depending on the model, the amplifier and its settings, etc. Humbuckers have a fatter sound, but at the same time let less twang through. The twang is that Buddy Holly sound. The fat humbucker sound is your Eric Clapton in Cream sound. But a single coil can also sound fat, but still just more twangy (Derek and the Dominoes Layla/ anything from Hendrix).
If you like Les Pauls, you can get them with two humbuckers, with humbuckers that can split up into single coils, or with P90 single coil pickups. As bob said, the P90 is a different kettle of fish from either humbuckers or normal single-coils (Stratocaster single coils), and has a big fat sound, a bit like a humbucker, with less twang than a single coil, but with more "articulation" (like the twang made less zingy ?).
If you've heard The Who's Live at Leeds album (and I suggest you listen to some of the tracks on Youtube) you'll hear what P90 pickups are all about (in a Gibson SG this time).
If you go for a Les Paul, what you get will depend on how much money you have. I have two, a Gibson Les Paul with P90 pickups, and a Tokai Les Paul with humbucking pickups. Gibsons are very expensive in SA, and it's wiser to buy them second hand (about R15,000 is what you should expect to pay). The Tokais - which I'm a big proponent of - are Japanese made clones, that offer Gibson quality at much lower prices minus the Gibson name. They are not available much second hand (if you can find one you'd expect to pay about R7,000), but new you should pay around 10 grand. Cheaper still are the Epiphones, which are Gibson's cheaper brand. These are available between R2,500 - R5,000. But quality varies a lot on these guitars as they're not all made in the same place to the same specs. They are quite cheap new now, but the latest ones are not good in my opinion.
In terms of whammy bars, it is quite possible to install them on a Les Paul, although it's very rare to find one to buy with a pre-installed system. Your option are:
Floyd Rose: This is the most powerful vibrato bridge. It locks the strings in place at the headstock so tuning is rock solid. This makes it more difficult to change strings, and if you break one, the whole guitar goes out of tune. But it does allow you to do any kind of intense vibrato work with no chance of going out of tune. People playing the "classic rock" that you like, usually don't go for them - although there's no particular reason why not. They're mostly associated with very fast modern styles.
Kahlers: Also very powerful, but not as favoured as the Floyd, not as stable in tuning, and some report issues with unevenness in the dips.
Bigsby: A bigsby is a very old-fashioned type. It can only do very subtle bends and can give tuning problems if not set up right. But they have a particular sound which is unique - the sound of '50s rock, and quite a few '60s players too. They're the easiest to install because they don't require any wood to be cut out.
This is Keith Richards's old LP:
Any of these units can be installed on any kind of Les Paul. I currently have a Bigsby arm waiting for when I have the spare loot to get it put on (it's getting to be a while now). Apart from getting those liquid '50s vibrato dips, I reckon these things just look awesome on a Les Paul. But that's just personal taste.