Like others who have posted before me, yes, I'd say the first step is to get in touch with some mortgage brokers to sort out what your options are.
You'll also want to get pre-qualified / pre-approved for a loan so you know what your price range is going to be. This will prevent you from spending time research properties priced out of your range. Also, some agents may not want to show you properties unless you have the pre-approval letter. In their minds, without this letter, you could be wasting their time if you later don't qualify for financing and the deal falls through because of it.
I went the FHA route for my first property, a triplex, and was also very concerned about out of pocket costs. There is the 3.5% down payment, of course. Typically, the home inspection, pest inspection, roof inspection, etc. are paid for out of pocket—but you might be able to negotiate to have the various providers paid through escrow (closing time). Prices for these reports vary. Here in California, I think I paid around $300 for the home inspection, around $200 for the pest inspection and around $100 for the roof inspection.
The appraisal process for FHA is a real bear. FHA appraisers are very concerned about (perceived) health and safety issues, and will "fail" a property if there are broken windows, mold, unsafe living conditions, etc. etc. Since you are wanting to do a 203k where these issues might exist, I'm not sure what the protocol is. (I didn't do a 203k.) But for straight FHA, if any of these issues are found, the seller has to fix them and then the appraiser comes back to the property—and you have to pay for the re-inspection! I was told initially that the appraisal would be $750. The appraiser ended up having to come back TWICE at a cost of $100 each additional time. So it cost me nearly $1,000. Argh. I was lucky enough to have this expense paid by the mortgage company, but I had to reimburse them at the close of escrow. In other cases, this could be an out-of-pocket expense, which is why I mention it here. Ask your lender who pays for the appraisal.
Lastly, for a 3- or 4-unit property purchased with FHA, you are required to have 3-4 months of reserve funds. This means that you take your monthly PITI payment (principal, interest, property taxes and insurance) and multiply it by 3 or 4, depending on what your lender requires. For example, my monthly PITI payment is $1,133, so I had to put up around $3,500 in reserves.
That's all I've got! If you have more questions or want to talk about FHA, please send me a message. Best of luck to you!
Erin