You are correct that FHA does have lower rates that a conventional loan, but you will have Mortgage Insurance...for the life of the loan. If you do put 20% down I would bet a conventional loan will have a lower monthly payment.
If you are concerned about closing costs you can always ask the seller to contribute x% (Limit is 6%, "norm" is 3%) at closing to cover them. You finance more, but you have less out of pocket. Or your lender should be able to have them covered in the loan, but that will raise the interest rate a little. A good lender can go over the options they have with you to cover costs and you can see what works best for you.
FHA 203k loans are not the only rehab loans out there. The conventional product is the HomeStyle Renovation loan, works almost exactly like the FHA 203k. Not too many brokers want to deal with them, but it really is not too difficult, other than more paperwork and a longer closing process. MI drops off at 80% Loan to Value, but it sounds like you would be putting 20% down so it would be moot. The big issue with either reno loan, at least for you, is that you can not do the work that the loan will be used for. You need to have a contractor do the work and have an appraisal done showing all work is completed. You also are "required" to have all the work completed in 90 days, I have had some go longer, but there were reasons that drew it out and the lender needed to approve . If you plan to do the work yourself, I would probably not go that route.
Putting less down and going conventional with MI might be a great route for you. Once you have completed your renovations (using the down payment you have) you can have the lender remove MI after the LTV is less than 80%. That way you can choose what work you will do and at your own pace. You would probably need to have another appraisal, but the long term savings would make it pencil out.
Good Luck