I just did something like that on a 1967 Mustang a friend's wife got from her parents. They needed to ship it to NY from FL and so I got it running for them so the shipper could move it on and off the transport. It is a 289 2 bbl/C4 car, so it may be similar to yours. Anyhow, to get it going, I would install a clear fuel filter in line between the pump and tank to see if the gas is contaminated with rust, and to make sure the fuel pump is still working . It may be that it will still run on what is in the tank, so you may be able to just idle it till it runs out instead of having to go through the hassle of disposing of old gas, which is hazardous waste. Then, if there is rust in the filter after you run it out, you can replace the tank (AKA trunk floor!) easily too. Also, the rubber fuel lines should be changed as well since a rupture could cause a fire. Anyhow, I agree with pulling all 8 plugs, and squirting oil in each cylinder. I also agree with priming it. Where I will differ is that after priming, I would try to spin it over by hand first by turning the crank with a socket wrench. With the plugs still out, I would next spin it with the starter and wait until the oil light goes out (distributor installed, of course!). This is to be sure the bearings have oil on them before they get loaded with cylinder pressure. The carb is likely out to lunch from sitting, so go ahead and get a cheap rebuild kit and go through it (this is the most likely reason it would not stay running). Yeah, do the plug wires and plugs too. I would also at least clean the cap and rotor terminals as well as cleaning (or replacing) the points and condenser. If you have a U pull it yard, go get a battery there as it will probably be under $20. Either that, or some parts stores have em used and cheap too. At any rate, it sounds like you have a nice project car on your hands! They make good projects because they are awful cars in stock form as far as the brakes and suspension go (Just like ANY 60's car). Then again, they look good and have tons of parts available to fix their numerous shortcomings. Out of curiosity, what are some of the specifics on it? Is it a Fastback, Convertible or notchback? What engine/ trans does it have?
1985 Cutlass Supreme Brougham (ex pizza delivery beater with 240,000 miles):
355 Chevy- 9.5:1 compression, Comp XE 262 cam, World S/R Torquer heads with 2.02's, Edelbrock Performer, 800CFM Q jet, Camaro ram air system,Edelbrock headers, Comp Magnum roller tip rockers,TH 200 4R, 3.23 rear, aluminum hood, IROC steering box, poly bushings, Eibach springs, etc. Cutlass build thread here: viewtopic.php?t=4982
Also: The Thing That Won't Die-1998 Nissan Frontier, 340,000 miles of pizza delivery.