Questions from a first time buyer in Chicago

Hello BP. Been listening to the podcast for a longtime and new to the thread. Been reading a lot of books, doing a lot of homework and I have some questions. I'd like to preface these by saying that I'm in the Chicago market and from the research I've done it seems it is much more difficult to cash flow going the multi-family building route with an FHA loan, which is what I'm trying to do. Here's what I got though.

1. Is it concerning that I'm starting to invest when the market is at a peak and facing a correction?

2. My top budget is $400k, and in this market can only afford me a 2 unit multi-family building. So should I start with a 2-unit multi family building (at $400k or less) or buy a $200k single family property that is in my budget , rehab it, and hold it until I have enough cash saved & equityto afford a 3 unit multi family that can give me a positive cash flow?

3. Assuming I don't buy a house in turn-key condition, what type of loan do I get to be able to afford the rehab that is required?

I know these are very specific questions, but I'm just trying to avoid as many first time mistakes as possible. I look forward to networking with people from my area, and I will definitely be at the meet ups!