Could be lots of causes. Did the bike start right up and idle well before you trailered it home? Did you go for a test ride of a few miles without any problems?
Poor starting and/or engine dying can come from a number of sources:
1) Crappy fuel. If left for over a month without stabilizers, fuel can degrade, water can condense and phase separate, rust can form and all sorts of things can get varnished up. The result is a product that my not burn or will plug jets etc. Best advice for a bike sitting a long time is to dump the tank, inspect the insides carefully for rust and particulate, and then refill it will good old fresh 87 octane. You can also add some Seafoam, STP or Techron to it, which you can find it at most auto parts stores.
2) Idle speed too low. If this is your problem, normally it will start up and run while you give it throttle but die when you lay off throttle. Since you said you were choking it at start we'll rule that out. (Even here in Florida where it rarely drops below 60 degrees, I have to give it some choke in the morning.) The idle speed screw is on the left hand side.
3) Idle mixture too lean. This can be remedied simply by removing the brass plug and richening the mix. Even if your problem is bad gas or idle speed, I'd recommend this mod anyway. Price=free.
It's documented here ;>
http://suzukisavage.com/cgi-bin/YaBB.pl?num=12218188224) Poor fuel flow. The savage has a vacuum petcock and notoriously crappy vac hose. IF the hose is cracked you may not see it and it may work sometimes and then fail other times. Best advice is to buy a 1 foot length of automotive vac line (same ID, thicker OD and get matching clamps). Lots of info on here about troubleshooting vac petc0ck probs, but if it runs on PRI but not on ON or RES you may have a bad hose or a bad petc0ck.
If you confirm that the petc0ck is working fine, you may have a carb float that is not working right, So even though the fuel flows to it, it cuts off the fuel too soon and your bowl is starved.
If the bowl is filled properly, then you could have gummed up jets.
5) Plugged air filter. Good idea to take it out and clean it anyway. Always remember to blow the air from the clean side near the carb to towards the dirty side where the air comes in.
6) Poor ignition. Spark plug removal and inspection is a good idea. From looking at it and smelling it you can get an idea if it is rich, lean or even if the PO replaced the plug with the wrong one.
Surely there are more things to consider but these should be part of any new bike inspection. The good news is that the Savage is a pretty robust bike and bounces back from moderate abuse very quickly. Good luck and keep us posted on your progress.
If you don't have your Clymers yet you can Google it and find electronic copies online until your book gets here.
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