Relocating from Texas to Chicago

I live right at the corner of Lincoln Square and Irving Park, currently.
Some of the best CPS schools in the city are in this area (Bell, Coonley, Lane Tech). If you buy in the zone for that school, you are able to attend.
You can also petition/apply to attend a school outside of your zone, it's just a very few that are accepted.
My kids go to private school, as we applied to Bell and Coonley - both 3 blocks from us - and could not get in. The CPS option we are zoned into is 1 mile away, and not great, based on our standards.

I can't speak to the neighborhoods you are looking at, but as they are mostly on the northwest side, as am I, it's a very family friendly portion of town. My husband grew up right next to Edison Park (in Park Ridge) and it's a nice area with nice homes. We looked in Jefferson Park and Norwood Park originally (we moved from Bucktown), but decided that we would rather be closer in to the city. In the areas that you are looking...they have more of a suburban feel than a city feel.

Pricing has come down quite a bit with the housing crash, so you may want to reevaluate the areas that you are looking at. Just food for thought. If you need a realtor, feel free to PM me. We have a friend that runs TriView Properties and they've done a lovely job for us and friends over the years.

I've never heard of a 6 month lease...usually they are a year. We relocated to the suburbs of Chicago and had a temporary apartment - month to month - and it was $5K for 2bed/2bath. But we were in the suburbs so there are fewer rental options. Good-luck and welcome to Illinois!

We live west of Jefferson Park, in Belmont Terrace, and it is a nice middle class and affordable area to live. I grew up here. Norwood Park, Edgewater and Sauganash are much nicer areas, and have the best schools on the north and northwest side. Check out:
http://www.greatschools.org/illinois/chicago/
Oak Park (suburb) has great schools, but is too pricey to get one of those big beautiful homes. University Village is south west of the loop, and I am not familiar with its schools. Logan Park is on the near north side, and again I am not familiar with its schools. Lake Side is 10 miles south of the loop, and a new development, so I expect it to be pricey, and I can't tell you about its schools, either.
The rule of the city dictates that you must attend the schools of your district. If you want a certain school, you have to live within its boundaries.
As far as the charter schools, they are by lottery. Hundreds apply for a few positions. We applied to five of the nearest charter schools for our son starting kindergarten last September, and he won a position in only one of them. After a brief review of the area, we decided it was too rough a neighborhood, and we would have to drive him there, since there is no school bus service, and we both work.
But I am sure you will find a great neighborhood with great schools, if you do a little research! Welcome to Chicago!

I would try a radius of 15-20 miles from where is his job is going to be.

I failed the math on thait one.. I live in Countryside, and work in Schaumburg..

I can say that the schools in Brookfield, and countside/lagrange are good. but moving.. look at taxes, and the high school.. those seem to be the tricky ones.

I recommend the blog CPS Obsessed for great CPS school info. The areas that you're mentioning are quite different from one another- some suburban feeling, while Edwater and University Village are pretty urban. As far as schools go, you can test into or play the lottery to get into schools across the system but you will want to make sure that your fall back schools (or neighborhood schools K-12) are ones that you are comfortable with. Be aware that many families do not get into schools that they apply to-- some schools literally receive thousands of applications. Good luck with your move!