Let's get honest here. You will find condo rentals and home rentals throughout the entire city. Burbank isn't broken into a number of smaller neighborhoods either. In fact, it has one major neighborhood designation and that's Scottsdale.
Scottsdale: Home to about 4300 homes. You will find home rentals, condo rentals, and a few apartment rentals here.
What's life like in Burbank? From the garage sales to the large spacious yards with some of the homes, this is typical suburban life. There's also a moderately sized parks division here. You're close enough to the golf courses and Chicago sports, but getting into town (or out of it after a game) can be a long process.
Plan to rent an apartment at least two months prior to moving in, and you'll need to take some time to browse the options before that. The city has a number of apartments available on an ongoing basis. Most landlords here do require employment verification, credit scores that are good or better, and a good rental history. It will not be easy to find an apartment with utilities included in Burbank, but there are some options that are out there.