I would go with an s rotor or Savonious for my turbine and probably the rope pump for starters. Two posts set in the ground with cross braces top and bottom for the bearings for the S rotor. 1 or 2 layers with 3 half barrels per layer if trying to keep it short. 3 layers of 2 half barrels per layer overlapped by 25-50% if height isn't a problem(about 3 meters tall). You can cut circles out of plywood for mounting or use whatever works for base and top (unless you plan on using the edge of a circle of plywood for a drive surface). It just needs to be something the half barrels and bearings or shafts can mount to(from my experience I would use a pipe down the middle for a shaft both for pto and to align bearings. For low tech try using wood blocks soaked/boiled in used motor oil with proper size hole drilled out first. Put a rock on it so it will not float while soaking/cooking. I would cut it in half using bolts to hold it together so you can adjust the fit and pack it with grease. Stack several large washers greased up between the bottom bearing and the turbine. I have seen old ag bearings made this way that and they work better than you can believe at low rpms.

For the pump part I went looking and here is what I find.

The air pump will not work unless there is enough water depth. To use air bubbling in the pipe for lift you need almost as much depth in standing water as you are trying to lift. To lift water 3 meters you need 2 or 3 meters of pipe in the ground with water in it. I don't know how much water this makes but 1000 liters in three days isn't much. Use 3/4 or 1" pipe(2 to 2 1/2 cm) for the water riser pipe and use 1/2(1 1/2 cm) or smaller for the air line flexable tubing will work. It needs to vent inside of the water pipe about 6" (15cm) above the bottom. This maybe a good option for later and should probably be used with a hawt as the prop makes the rpms needed to run the air compressor.

A piston pump might work best. Use a disk attached to a shaft from the bottom. Make an offset pivot point (like the old steam trains) Use flexable tubing for next joint just before entering pump. Pipe or rod must fit snug to reduce water loss or have packing, if pipe is used it must be plugged. A rubber flap for a check valve for incoming water and a marble or something like it for a check valve for the outgoing water(this only works if this pipe is pointed up).

With the offset pulleys and twisted belt it changes the plane of rotation and the rope pump can be driven from it. You could also run the edge of a plywood circle on an other wheel but you might need to cover the edge with rubber or something for traction.

A windmill type pump could be used with setup too. It is just a variation of the other piston pump. It is one pipe with a flap or ball check valve in the bottom. A snug or tight fitting pipe that slides inside with a ball check in the bottom of that pipe. The inside pipe carries the water in this version with an elbow at the top leading to the tank. The larger pipe can be capped at the bottom and a suitable hole drilled for the ball or the flap to seat on. The smaller pipe that moves should have an even smaller piece of pipe glued into it and a marble or ball that rolls easy in the moving pipe but will not go into the smaller piece. This setup would need to have several feet of smaller pvc pipe above the larger pipe so that it can flex and will need an outside clamp on the movable pipe or some suitable arrangement.

A gear pump or other postive displacement pump that gives the needed output at low rpms could be used too but would need to work with water ie not corrode. For this you would need to check locally.

All pipe and pump parts need to be plastic or glass or nonrustable. Your storage tank needs a filter before going into the drip lines. Are you using above ground lines? drip or soaker lines? If your water is alkali then vinegar and and ammonia(not sudsy needs to be just ammonia) can be run diluted into the lines to help clean them. The vinegar will help with ph and the ammonia is fertlizer.