Although many banks will do a 203k loan, not all bankers explain the 203k loan to buyers adequately in my experience. I would suggest that you speak to a few bankers who specialize in 203k loans almost exclusively. 203k loans will most definitely allow you to fix up a home within your budget but they have added expenses - for example, there are minimally 4 added appraisals. Basically these are bank inspectors who appraise the work completed and authorize that the contractor is paid. So it's a bit of an added expense but also ensures that the work is completed before the contractor is paid.
In my view you need 3 things - a banker who specializes in 203k loans and can explain them to you fully, a contractor who has the financial ability to do the work first and then get paid and an attorney who understands the 203k process so you can be advised correctly on that level.
With short sales, the most critical component is your attorney. If you do not have an attorney who is absolutely expert in short sales you are not, in my opinion, adequately protected no matter how knowledgeble your real estate agent may be. Remember always that in buying a home in Bergen County, you are using sales contracts and only an attorney can adequately represent you on such matters. Having a real estate agent who is adept at short sales is also critically important but the most urgent need is that of an attorney who is expert at short sales whether you are a buyer or seller.