What is also suggested to replace when replacing the water pump?
If the car in question has a timing belt that is driving the water pump, I would in all cases replace the timing belt along with the water pump. It would be just stupid to reuse such a cheap belt, when you need to anyway remove and reinstall it. Especially considering that timing belts have a regular replacement interval and the results of a failing timing belt can be catastrophic.
However, this applies to cars that have the water pump driven by the timing belt. Not all cars do: in some cars, it may be driven by a separate accessory belt (I would replace the separate accessory belt then, no reason to reuse an existing belt). It may also be electrically driven, like in Prius. But your Solara doesn't have an electric water pump.
I can't say if your car has a timing belt or chain (V6 has belt, and I4 has chain). But as a general rule, replacement of the belt is a good idea no matter whether it's an accessory belt or the timing belt. The only exception to this rule is if the belt has been very recently replaced already.
I wouldn't change the thermostat unless there's some demonstrated issue with it.