Pounded quite a few 'points years ago, by hand. Talk about fun.
Don't spend money on a pump until you do the following:
Did you use drive couplings? Drive couplings are over-cut and look very different (internally) from a normal 1 1/4" galv coupling. Also, did you use a drive cap when pounding down the sections. A drive cap has the same taper as the drive couplings. Drive caps are easily identified by a drilled hole in the top of them.
If drive couplings and cap were not used, you've probably split the threads on the pipe. If that is the case, pull it back out and re-cut the threads, also inspect the threads on the point itself. If you didn't use drive couplings, get another point. Think about drinking a milk shake and your straw has a hole in it.
You see that old cistern pump that Speedbump has as his avatar? You want one of those to 'develop' the well. Just make sure to soak the pump in a 5 gallon bucket to get the leathers to swell. Prime the well and pump it for all its worth. A good 15 minutes of hand pumping will help to clear any clay from around the point, which in turn will provide for easier pumping and greater well capacity. The cistern pump will move much more water than your shallow well pump will, but your shoulder will get sore doing it. The amount of resistance on the handle is a good indicator of the amount of water in the area of your sandpoint, and also an indicator of whether you have a leak in your drop pipe. Resistance is good at first, as it means your drop pipe is not sucking air. Some wells I've pounded have taken all my 180# on the handle to get them to go, but, after a thorough pumping they've freed-up and produce good volume with minimal effort. Minimal resistance (with poor water volume) is almost always a bad sign, as you're sucking air. If you're able to pump water but the handpump loses its prime quickly, look at your fittings and drop pipe.
Now, before you go pulling that point, run a 25' tape down the pipe, or a string with a small weight attatched. You want to find the static level of the water table where your well is. You should have at least 4'-6' of water in the bottom of that pipe, and that's figuring a poor well.
If you've done the hand pump and checked your static level is low, find a new location for the point. Also, be as far as possible away from any drainage piping/septic tank/drainfield. Minimum 50'.
Why two check valves? You should only need one just before the pump, preferably on the well side of the union. That way, if the union were to leak, it will be on the pressure side of the check, and suction within the well could be maintained.
Good luck.