All pretty good sound advice above, but I wouldn't worry too much about a new carb. kit just yet. Out of the 30 some old tractors I've had over the years, only one needed a kit,and that was because someone ran the main jet in too far, and damaged the end. The bowl gasket may get dampish, but will more than likely seal off, once it has contact with gas again. Make sure the sediment bowl, and screen above it are clean. You should have good flow to the carb. Do remove the elbow going into the carb., the fuel line attaches to. There is an internal fine mesh screen that is usually where some sediment will collect. Spray it with carb cleaner from the outside, and finish with some compressed air.
Might be an idea to remove the carb., and drop the bowl. Setting that long, there is probably some rust and sediment in there. Remove the main jet, and spray through all of the ports. Put the main jet back in, and run in until you just feel it seat, go easy on that part, then back out 1-1/2 turns. Ought to be close enough to start. You can tweek from there once it starts. Just be careful putting the bowl back on not to bump the float, and get it out of adjustment.
When you put the battery in, and if it is still original 6V, don't forget that it is positive ground. If you have a test light, go ahead and get the ground end hooked up. With the switch on, touch it to the input side of the coil to make sure you have current to there. Then test the output side going to the distributor. Just don't leave the switch on very long, in case the points are making contact. Don't want to burn them.
Pull the distributor cap, and check the lugs for buildup on them. Ionization can cause a carbon buildup on them. If it has brass lugs, it will have a brown/black buildup on them, if aluminum lugs, it will have a whitish/green buildup. You can scrape that off with pen knife to get by. Also pull & check the rotor button, it too will probably have a bit of tarnish on it. Some fine sand paper, or scrape it with your knife will clean it up too. There should be a cover between the rotor button and points. Pull it off to see the points. If you can roll the engine over by hand, until the points make contact. You can then turn the switch on, and take a screw driver, and work the points, to check if you have spark there. Again, only momentarily, so you don't burn them. If no spark there, odds are, the condenser is bad. If you have a good bright trouble light, or small bright flashlight, you can open the points, with a smaller screwdriver, and somewhat see the condition of the points, as to whether they are burned. If they don't look the best, get a new set, and condenser. Get a decent set like Echlins from NAPA, or OEM's. The cheapie sets, wear blocks don't seem to last long. One of those small 2-3 inch long screw starters are the handiest to thing to get the screws back in. If you don't have one, get the one with the magnet on the other end. The long ones don't work in that spot well, as they hit the oil filter canister. A good flat stubby screwdriver to snug the screws. Set the points at .020".
Might as well clean the plugs too. Check & set @ .025"
If the oil was pretty dirty, might be an idea to replace the oil filter. When you take the canister off, there will be a square shoulder o-ring in the groove, where the canister seats. You'll need to remove that, and replace it with the new one that comes with the new filter. I have an ice pick I use to remove that o-ring.
If you have spark, fuel, and air, she ought to fire up, or at least get a pop out of it.
Depending on the temperature, unless it's really cold, it shouldn't take a lot of choke to get it started, once the fuel bowl is full. Maybe 3-4 revolutions at full choke, and throttle set about 1/3. It will let you know if you've choked it too long, as gas will drip from the carb.
Good luck..!!
