Any advice for work balance?

I recently signed with a modeling agency — and not just a small one, one of the biggest agencies in the world. Since signing, they’ve already been sending me castings and jobs, which is exciting, but a lot of them are in other states and require flights/travel, sometimes on really short notice.
The thing is, I still work a normal job that pays my bills, so I can’t realistically just drop everything and leave whenever a casting pops up. Right now, since I’m still new to modeling, I can really only take local jobs or things that fit around my days off.
When I signed, they told me they’d work around my schedule, but I’m worried about constantly turning things down and being seen as lazy, difficult, or not serious about modeling. I don’t want to become “the guy who always refuses castings.”
I’m also a little confused about what jobs I should and shouldn’t be taking this early on. Part of me feels like I should say yes to everything to build experience, but another part of me worries about the type of work I’m doing. For example, if I start doing commercial/non-fashion jobs like Party City, random retail campaigns, etc., could that hurt me long term if I eventually want to move more into fashion/editorial/high-end work? Or is that not really how it works?
Basically I’m trying to figure out:
How selective should a newer model be?
Is it normal to turn down travel jobs because of a regular job/life responsibilities?
Do agencies get annoyed if you can’t travel often at first?
Can doing too much commercial work hurt your future image/career direction?
How do you balance modeling with a normal job when you’re just starting out?
Would really appreciate insight from people actually in the industry because I’m trying to approach this professionally and realistically.