I think what Gifford means is pictures under the rockers, in the trunk, at the suspension mounts, engine bay, all the areas where rust or bad repairs might be. That information can swing the value 100% one way or the other.
Also review Giuliettas.com from Matt Hamilton to find comps.
Whatever the initial cost is, it'll be a fraction of what you spend afterward. If this car has typical body issues, not fixed yet, it'll have a holey trunk floor, rocker and floor issues, front valance issues, bumper area issues at the back, etc. Unless you can do that bodywork yourself, you can easily spend into five figures on body repair alone.
My guess/ballpark without knowing more is $5000 tops.
The price depends on what your ultimate aim is - 100% original or a neat driver with a leaning towards originality ??
The shell you showed is either a late '58 or an early '59 Interim or Transition version, remember that in the US cars were dated as the year in which they were titled - it has the 750 jack-point-in-sill and would have run a 750 motor and either a tunnel case (before September '58) or split case transmission (after September '58) - in your case lets hope it was a split case as they are much easier and cheaper to find and you won't have to modify the tunnel floor.
I agree with Andrew, they virtually all have rust issues in some form or another - some minimal and some deep-seated. This car has the open sills, so they should have survived better than a closed sill car, but I'm with him on the boot floor, the floorboards and the front valance, if not the whole nose cone but don't let that put you off, I have no formal training in mechanics or bodywork & I do just fine.
It's the missing bits that would concern me, a suitable motor & box are simple to source provided that you are not absolutely focussed on originality - if you are....kerchingggg $$$. It's the missing 5% that concerns me more, your "missing ... couple misc.", on a 2000lb car that works out to 100lbs, or 50kg's and that's a lot of weight when you start adding up alloy trim bits that were made of unobtanium when new. Virtually everything is available, either new or second hand, but co$t$ add up quickly.
It's not an exact comparison by any means, but this early 6" headlight car on ebay will give some guidance on value if it makes its reserve. It also is instructive to look at the problems areas on this car, which are pretty well pictured, for what most Sprint restorers are in for on rough/incomplete cars. Alfa Romeo - eBay (item 220758395311 end time Mar-31-11 17:58:43 PDT)
Thanks everyone for their response and advice, I was looking into buying this car, but I wasn't sure exactly what to expect with this car with costs associated with restoration and finding parts. I will keep you posted on the result.