Hi @Ashlee Reimer my advice would be to hook up with someone (as you can see, you've already found several potential contacts here on BP!) that knows that part or really all of Chicago very well and who can advise you on what you're looking at and what your goals are, how much you're looking to spend, etc, etc.
Not trying to be nitpicky, but even when you say that you're looking at the "south east" part of Chicago, you're still talking about a HUGE area! I've never been to the Vancouver area (I've heard its a great place to visit for many reasons though!) but I looked it up and the entire Vancouver metro area is about 2.5 million people. Chicago itself has 2.7 million residents, metro area has 9.5M, so you're talking about a city or metro that's 4 times the size of the Vancouver metro, its BIG! Also, the south side of Chicago, as I and others have mentioned has a very wide variance in neighborhoods, residents, etc. For instance, President Obama's house (not the big white one in DC, but his actual family home!) is in Hyde Park, a really cool area on the south side of Chicago, full of lots of beautiful older homes as well as apartments and condos that sell for a lot of money. Yet, you can drive just a little ways, blocks even and be into some pretty darn sketchy areas where you really have to watch your back. Last time I checked, they still don't make maps yet that show where "the hood" is!
Again, don't take me the wrong way here, not trying to discourage you one bit, but is there a particular draw for you to Chicago? Besides what others have mentioned about the Cook County landlord laws, the nice or even average parts of Chicago are very expensive places to buy property in. I know Vancouver is a nice place to live, I have a large number of extended family members who've lived in and around Seattle for many years, but I'd think that Chicago would actually end up being even more expensive-IN THE NICE PARTS! Some parts of the Gold Coast on the north side have areas where houses regularly sell for $5M, $10M or more. (although they are VERY nice houses!) I guess I'm wondering a bit why you wouldn't want to invest in a mid sized are like Milwaukee, Minneapolis, Indianapolis, etc where you can get in for less? I'd think that the only pricier cities in the US would be NYC, LA, San Francisco, not sure where else would be pricier than Chi-town, unless of course you're talking about buying "in the hood"!
So, my advice would be to hook up with someone soon that can educate you as to where you're looking and what these areas are really like. Otherwise, I think you're just really spinning your wheels looking at what's for sale and how much rents are without knowing if you're buying in a decent area or a warzone.
Having said that, good luck on your future plans, I do have to say that I admire your ambition for looking to invest elsewhere!