Sparks are not uncommon when reconnecting a battery. Typically, you want to make sure the key is set to off, connect the positive, then connect the negative last. (Reverse is true for disconnecting, always remove the negative first). This cuts down the chances of inadvertently shorting your positive to the ground when wrenching on the positive terminal.
First check park brake is set, PTO off, in neutral, and seat safety switch. If all those are working, you should hear a clicking noise. Sometimes you have to press the brake further than where park is set, sometimes need to wiggle shifter and clanck to left to make sure neutral switch is tripped, PTO left on is very common (especially after running out of gas while mowing), Seat switch is easy enough to short out with a jumper wire.
There are a few tests you can try with a voltmeter. One sounds like you have done, and that is to see if one of the big wire to the ground has 12 ish volts, the other will have zero. With weight on the seat, turn-key and see if the zero side goes positive. If does go positive, it's likely a starter problem. Disconnect everything and figure a way to spin the starter manually with a long screwdriver or something. Sometimes, brushes get bad spots and simply rotating the position will engage the magnets.
If the starter side of the solenoid didn't go to 12 in the previous step, move your positive probe to the smaller wire going to the solenoid. If it goes nowhere when flicking the key to start, then start jumping safety switches.
Does your tractor have a supplemental "Starter Relay" installed? Google AM107421 Sometimes the solenoid doesn't get enough juice from the ignition switch to engage. Wiggling the wires probably used to be enough to get past the hump.
This Minor fix is very common. See more here:
I bought a generic version of AM107421 for about $10 or $15 on amazon or ebay.
Here is a $30 version from JD of Ebay:
Before you shell out for this, another quick test would be to make a jump start lead connected to the positive and touch the other end to the small wire going into solenoid (as in the little wire that is not grounded). Or jam a screwdriver across the two big wires on the solenoid, that will throw a few sparks, but the started should spin.
Hope one of these works for you.