I had a bumpersticker on my full-size F-150 pickup (recently sold) that read:
"Yes, this is my truck. No, I won't help you move."
Almost any pickup truck owner gave a knowing chuckle when they saw it.
Back on topic - I would recommend having a Class III hitch receiver installed on the S-10 if it has a V-6, or using a tow bar behind the truck if it has a 4 cylinder. Also, find out what engine is in the truck. A general guide to the towing capacities would be something like this:
4-cylinder - 2,000 lb./200 hitch weight
2.8L V6 - 3,000 lb./300 hitch weight
4.3L V6 - 4,500 lb./450 hitch weight
These aren't based on specific information I found on the web, and you should consult the truck's owners manual for more specific information, but these should serve as a general guideline. My wife has a Chevy Astro minivan (based on the S-10 chassis) with the 4.3L V6 and it is tow rated at
5,500lb./500 hitch weight. However, it does have a "Tow/Haul" mode on the tranny and additional cooling systems.
If the truck is a 2.8L engine, I would tend to shy away from it. The 2.8L was a somewhat trouble-prone engine. The 4.3L is literally 3/4ths of the venerable chevy 5.7L (350 cid) V-8 engine and is considerably stouter. The typical 4-banger in those days was the good ol' "Iron Duke" 2.5L engine, also a pretty stout piece.
I used my old F-150's step bumper hitch ball to pull a 1500 lb. flatbed trailer with several hundred pounds of household goods without incident the last time we moved. I was probably pushing 3000 lb. on a couple of trips and the last 1/2 mile to our house has a pretty steep grade. Still, I climbed that hill each time with my fingers crossed, hoping the trailer wouldn't rip the bumper off the truck.