Having lived in St. Louis prior to moving to Texas, you have to be cautious of where you go. Roxana is semi-OK, but there are areas just north (Alton) and south of there (East St. Louis) that you REALLY need to stay out of. Roxana proper has below average violent crime rates, but above average property crime. Alton is double the nation average and East St. Louis is almost 3 times on violent crime alone. Across the river in North St. Louis is also not a good area and has a higher crime rate than East St. Louis.
Don't let that scare you though. If you have been to Houston or Dallas, they have their bad areas too. Just talk to a few folks in the office you will be working in and find out where the good places to live and bad areas are to stay out of. There are plenty within a short drive, even if the area you work in is not the best. Edwardsville is not bad and a college town and pretty close.
As for gun laws, I would really take the other posters suggestion and contact the Illinois Rifle Association about possession. You will NOT be able to carry or have it loaded in your car in Illinois. However, Missouri has reciprocity with us, has car carry, and is actually open carry state unless a city ordinance prohibits it. If you can find place to live in Missouri and commute across, it might be better, but it would mean a fairly long drive and maybe through rough areas unarmed.
Here is a good resource for looking up demographics in general
http://www.bestplaces.net/.
Good luck!!
But what I wanted to know is if there is anything that I can do to be able to take my baby along with me? I read about guns in the vehicle have to be unloaded, ammo separate, and out of reach, but what about the FOID card? Is there an equivalent that non-residents can obtain? TIA
But what are the majority of the people there like? Is there really a need to have a gun with me? I grew up on the rice farm so if it is all farming communities around I wouldn't be too worried...? (I've never been outside of Tx 
