You've got a few issues here. All of which can either be simple or difficult depending on how you approach them. Getting multiple bids from GC's and contractors is obviously one of the easier options. You can do this now and get the ball rolling. However, that may or may not work out so well. Each GC or Sub will likely bid the job the way he thinks works out best. Often times clients end up with a whole bunch of bids that are apples to oranges.
Your two basic options to deal with this dilemma are to either put out a detailed RFP or Bid sheet or hire someone (like an experienced inspector) to decipher the various bids on an apples to apples basis. Putting out a bid sheet helps minimize differences because you are telling the contractors what you want bids on. However someone has to put that Bid sheet together for each trade. Anyway you go there are costs involved. The upfront costs are however typically far less than the potential costs during the job due to poor pre-planning.
Another issue you will face is the difference between what you think ONLY needs to be done and what may HAVE to get done in order to satisfy City Code requirements. There can be a pretty big difference. Any permit will also have to address any outstanding violations on the building. When interviewing GC's make sure their license is up to date and they don't owe any parking tickets. Both can hold up your permit.
As far as getting contractors interested, that's not a problem. Work is slow, everyone contractor out there is looking for a winter project to settle into.
If you are going to do this from out of state, I highly recommend you absolutely have an uninterested 3rd handle your affairs in regards to the project. Whether its an attorney, architect or inspector is up to you. Who is going to verify work completion and pay out approvals, who is going to verify quality and compliance, who is going to verify sign-offs with City inspectors?
I don't know what your resources or situation are. I dealt with this situation many times over the years as the clean-up guy for projects that went awry. If you have the financial resources and basic knowledge to pull this off, great go for it. However if you are inexperienced and financial resources are tight, consider putting together a plan to sell the building as-is and be done with it.
If you hire the right guys you should be Ok. If you hire the wrong guys you'll really be screwed more than you can imagine.
Basic full rehab cost $100 sq ft general estimate
Ballpark trade costs for say a new electrical service, furnace or plumbing per unit are all easily attainable. Drywall, tile, floor sanding are all fairly easy numbers. The carpentry tends to vary more extensively
Hope that helps