First of all, if you DON'T have anything resembling studio monitors to hear what you're doing with the synth, you have a problem. Secondly, if you have monitors without an amp, you REALLY have a problem. You cannot hook a modular synth up directly to a pair of speakers unless they're powered, and it doesn't sound like those are.
Second, there are some who use headphone-outs for their modular's audio out. I don't recommend this at all. For one thing, the headphone output can vary widely from one module that has that to another, but in all cases you're dealing with a preamplified (and NOT line-level) signal that also probably has an impedance mismatch between its output and whatever line-level input you're using. It's also not impossible for the headphone output to be DC-coupled, which as Garfield mentions, is quite bad...especially if any DC it's passing gets some amplification and then...well, this:
Thirdly, if you're still sussing out how to get audio out of your modular, I would suggest STOPPING those cash-dropping plans for a bit. I'm already hearing how you want to use a Rosie as a mixer...which it SORT OF is (it's more related to a DJ mixer/crossfader), but not necessarily in a way that's useful for all rigs. It also doesn't sound like you have a proper working environment set up, either...some sort of basic mixer might be useful, an amplifier for the whatever-those-speakers-are (the connectors are to connect the speakers to an amplifier, NOT for line-level signals at all), and so on. These are actually far simpler to sort out than the modular itself, so I've got some concerns as to what your build actually looks like and consists of.
It's EXTREMELY easy to get into an idea that you've got your build sorted out on a first (third, seventh, nineteenth) try and that you're ready to drop some plastic on it. Therefore, it's equally easy to wind up with a semi-functioning build due to that mindset., and also equally easy to be out a few grand when you pay for something that can only semi-function that leaves you wondering why it behaves lousy and sounds like refried poo. Note also that you've been "...reading up over the last month in preparation for my first rack purchase". That's almost certainly NOT long enough to properly come up with something with zero background and experience. Remember: Modulargrid is NOT a video game. There are no bonus scores for coming up with your build as quickly as possible...but there definitely can be one hellacious booby prize waiting if you think you can! You're talking about an investment in a few thousand $$$ here, after all.
One other thing I would suggest prior to coming back to this idea would be to actually get some experience at this via VCV Rack. That's a Eurorack emulator, with many modules that replicate operations (and even some actual modules) found in modular synthesis. It's also FREE, so it's definitely better to spend some time with VCV prior to dropping ANYTHING on physical hardware so that you've got some better ideas of what you actually need before this gets spendy. https://vcvrack.com/