I guess it kinda depends on whether you want to play loudly or not, and if you'll want to use the natural feedback from an amp to get some of those screaming lead sounds. An amp is responsible for a large majority of the tone you'll be getting and will actually help you improve your playing because you'll be 'getting into it' more if it sounds good through a decently loud amp.

Personally...I'd probably go for the monitors. However, only if I could get a really decent sound to begin with.
Like, I haven't used an amp to record with for years. Too much noise and too much hassle trying to mic them. But I have to use top of the line pickups in the guitar, expensive guitar cables, a Boss GT-8, Amplitube and a cabinet simulator to emulate the sound of a real amp.
The one thing that is the most frustrating is getting natural feedback on leads. You can get it on monitors but it's kind of a crap shoot as to whether it will work or not.
I used to have a pair of cheap old computer monitors that would give me screaming sustain that sounded like a Marshall stack. However, when I upgraded to a better sound system, all the sustain went away.
So here I am years later, still keeping my cheezy old speakers tucked away for when I need em.

Not sure what to suggest really. Like I said, I'd probably go for the monitors but that's because I spend a lot of time recording.
However, there's just nothing that can beat the sound of an amazing amp turned up nice and loud.