You can rent a EPIRB for well under $100 from the Boat US foundation. We did so for The Hook Race this year. For your trip, it's good insurance. However, I've done 6+ similar crossings. We chose not to rent one while cruising because we could always pick our weather window. But be careful, the lake is BIG and weather can come up unexpectedly!
I've personally skippered a bareboat twice from Monroe Harbor Chicago to New Buffalo, MI. It's a great little town. One main strip downtown. Beautiful beach with taller dunes and boardwalk to the top. A nice breakfast joint or two and one or two bar and grills (rooftop seating at the Stray Dog). A bit of nightlife.
Our boat was 30' and drew 4.5'. The harbor entrance and transient area is shallow, but we had no problem. Even if you scraped it seemed pretty darn sandy.
The whole offshore thing--on a clear day you might just barely lose sight of land between Chicago and New Buffalo. New Buffalo, in my mind, is the first port from Chicago that represents a true crossing. Michigan City, to me, feels pretty coastal.
You gotta' love Lake Michigan (as long as you respect her). For years, I did a bareboat charter "with the guys" each summer. One year, we had two days and everyone needed to be back at work on Monday--not a good recipe. Well, the forecast stunk--no severe storms but plenty of rain, wind (pushing 20 knots), and waves (5-7'). I honestly did NOT think that we'd leave Chicago. Well, the crew was moderately experienced and the boat pretty stiff. We poked out of Monroe Harbor and things felt good so we went to Michigan City. We really got the boat into a groove. That was the first time I ever saw someone truly green. Unfortunately, one of our crew got sick--really sick. Well, we put him on the train back to Chicago Saturday night.
On the way home Sunday, the weather was more of the same. Instead of a reach, our ride home was a very broad reach. We screamed (both in boat speed and literally) home! We FLEW into Chicago Harbor under double reefed mainsail and a sliver of jib. It was really a sense of accomplishment. We still talk about it (in case you haven't guessed!).