Northside is mostly all fine, many parts are kind of Bro'y or yuppie imo. Uptown will be affordable and its where the awesome and infamous wilson skatepark is. That area does have a fair share of mental people - just a warning. Lincoln Park is one of the best neighborhood imo, however its pricey. Pilsen and Bridegport are coo & affordable in "South Side", (theyre not very south). Otherwise stay away from southside or westside. Wicker and logan are cool, not cheap bc of that. Avondale is near but a little less nice/hip, so less $. Ukrainian village and near-west are safe cool and might be affordable. I used to live in Little Italy, its a nice neighborhood near downtown. No problem being car-less. Bus..train works, but bicycle is the best imo. My place was cheap because it was 100 year old and falling apart. If you want your own place in a nice hood it will be well over 1k. Otherwise with roommates you can go under.
When I lived in Chocago my strategy was find the cheapest shittiest apartment in the nicest neighborhood thats most convenient for School/Work commute.
Each place has its own vibe and you have to figure out which is best for you with all things considered.