@OP, I am a solo female traveler, too. In April and May I went cross-country (Los Angeles to New Jersey) alone on Amtrak, and it was my first long distance train trip ever. I was a little nervous about things, like you are, but let me tell you it's SOOOO much easier in person than it sounds from reading about it online. Upon arrival in Chicago, I had a redcap meet me at the train and take me to the Metropolitan Lounge. All you have to do is let your SCA know you need a redcap.
Once you get to the Metropolitan Lounge, you just have to show your ticket at the desk to gain access. Let them know that you want a redcap when it's time to board. I was even asked what time I wanted my first meal on the train (dinner, in my case) and the reservation was forwarded to the train staff on board.
The lounge was much larger than I expected, with many many comfortable seats. Just inside the door, near the check-in desk is a place to leave your luggage so you don't need to bring it all the way into the lounge. There were a very few snack foods, plus coffee, etc. Nothing to make into a meal. There's a food court in the station, though. You cannot bring outside food into the lounge. I didn't use the showers last time, but I'm hoping I'll have time on my upcoming trip.
Before it's time to board, there will be a very clear announcement that people who need redcaps for your train should come forward.
I stayed at the HI Chicago Hostel for 4 nights. I "splurged" on a single room with a shared bathroom, I believe it was about $100/night . My room actually had 2 beds in it, and more than enough space. I know you said you're not interested in exploring Chicago, but it's right in the heart of things if you change your mind. There's a Panera half a block away, and a restaurant right at the ground floor of the Hostel. I felt very comfortable at the hostel, which is really much more like a hotel than I expected. There were 3 other bedrooms that were to share the same bathroom, but I never saw anyone else in there at all.
Anyway, I liked being on the train so much that I'm gearing up for another long trip next week: Grand Junction, CO -> Chicago -> Washington, DC -> Baltimore -> New Jersey.