If you have a front wheel drive, access to most items is restricted and more should be changed. Above are great for a standard North - South arrangement but say a PT Cruiser has access issues and more should be changed along with the pump like the timing belt.
OP has a '90 Horizon if the Avatar is to be believed.
As I recall the water pump is actually two parts. The pump with impeller and the mounting assembly. The assembly is not normally replaced - just the pump itself. Should be a gasket included with the pump. But given the age of the vehicle it would not be a bad idea to replace both if parts are available.
Otherwise, I would consider replacing all hoses, clamps, coolant (of course), thermostat, etc while the system is apart. Might want to flush the system as well. Swap the heater hoses to the heater core and reverse flush to remove any crap that has built up over time just be careful removing the hoses. The last thing you want to do is replace the heater core - not easily replaced. Might want to upgrade the coolant to HOAT (Zerex G-05), but the cooling system needs to be totally flushed. Don't want to mix coolant types. The HOAT G-05 is designed to last 5 years vs 3 years for the traditional green coolant.
The water pump on this engine is not driven by the timing belt, but the serpentine belt if I recall correctly.
Timing belt should be changed every 105K miles as I recall - check the owner's manual if you have it. If it does break, the engine is a non-interference design so there won't be any valve damage if/when it breaks. Just install a new belt, check & set the timing and you should be good.
I changed the water pump on a '90 Acclaim 2.5L and it took me about 3+ hours in my driveway. Not a complex job, but it was time consuming. I recall having to remove all the belts (serpentine and alternator). Part of the issue on mine was the top bolt of the pump was behind a bracket which was part of the top engine mount. To loosen I had to support the engine and loosen the top engine mount to allow access to that top bolt. The Horizon may be different. It's been 30 years since I owned a Horizon.