Missouri Wind and Solar has a number of charge controllers and they have videos of using a pond aerator without batteries. It would take a bit more
energy to pump water uphill, but it can be done. They do have some programmable charge controllers for wind and solar which might work well for this. The one is designed to run a dump load once the batteries are fully charged. It probably won't work without any battery, but you could likely use a much smaller battery such as the type used in tiny computer UPS's or car battery booster packs to keep the electronics running. Then adjust the settings (engage dump load at a lower voltage, disconnect load from battery at a higher voltage) to run the pump as the dump load from the solar panel(s) instead of the small battery.
From what I understand, a lot of DC motors are not built to withstand a continuous load (3+ hours a day run time). I would either get a good brand DC pump like a
SHURflo, or get an A/C motor rated for continuous use and an inverter. It might be more expensive initially, but burning up a bunch of motors not up to the task would be far more expensive and frustrating in the long run.
The starting amperage of a motor is much higher than the amount of current used after it starts running. It might only be a few seconds, but without a sufficient amount of current being supplied it will never start. One interesting thing I have seen is
This Video on Supercapacitors. While that particular video shows it being used in a car, he has numerous videos about the supercapacitors and solar energy which are very interesting. If you were to use a programmable charge controller or design your own based on a microcontroller like an
Arduino or similar, you could set it up only start once you have sufficient energy and it would allow a small amount of run time in case a few puffy clouds shade the panel for a bit. I personally think this is better for mobile uses instead of stationary because it is lighter and much more expensive to implement, but it is noteworthy as the prices of supercapacitors go down over time.
You could go much further with this and look into systems such as ones available at
Open Sprinkler. They have systems based on the Arduino,
Raspberry Pi, and more. This takes a bit of learning, but it can make a system that is cheaper and more reliable in the end. Also, there are millions of people out there using these devices and you can usually find someone trying something close
enough to your plans that it can be easily adapted.
There are lots of places you can ask for help on this. There are tons of forums and websites that cater to microcontrollers, small computers, off grid
gardening and so on where you can find people doing very similar things. I have seen too many YouTube videos on this topic to list here. Do a search there for your keywords like solar, irrigation, and similar. I'm certain you can get a better idea of exactly what you need by checking out those places and most of the people doing it are glad to help.