Welcome, happy to have you! I haven’t read Shirokuma Cafe, but I did watch the anime a while back (to, uhh, questionable levels of comprehension). My understanding is that it is indeed a solid first pick, but just be aware that there are going to be some uncommon words that may not be too useful to you right now, because they love to do wordplay.
If you run into troubles or questions along the way, since you’re starting out, I’m sure someone would be happy to help 
Oh also, this manga was read by a book club in the past! Highly recommend checking out the thread. There you’ll find already assembled vocab lists, lots of questions you might have already answered, and usually people watch those threads even long after the official end, so Shirokuma Cafe specific questions posted there will probably get a quick answer even now.