Pipe size
As everyone has stated, you need to th eGPM that pump is putting out on that well. That can be done real easy using a 5 gal bucket, a ball valve, some PVC coming off the pump, and a watch with a second hand. Looked at your pics, this is something you can do in an hour .for about 10 bucs. Use 1 1/4 inch PVC and tee off your pipe to the tank with about 2ft of pipe, a tee with a pressure gage, then about 8" of pipe followed by the ball valve and 8" more pipe and a 90 ell. Measure the time it takes to fill the bucket at 45 psi and divide by 5. Do this three or 4 times and take an average. Now you know the GPM of your well at the pressure you used.
As for the pipe size going to your house in Texas 1000 ft away from the house, PVC is definitely your answer and hear are some pressure drop numbers to consider
1 " Schedule 40 PVC @ 12 GPM -3.36 PSI per 100 ft, @ 10 GPM 2.4 psi/100
1 1/4" Schedule 40 @ 12 GPM -0.89 psi per 100 ft, @ 10 GPM 0.63 psi/100
Galvanized 3/4" @ 10 10 GPM 16.46 psi per 100 ft
@ 5 GPM 4.56 psi per 100'
Fo those of ya'll that have never been here before, check out his pictures Texas hasn't been this green in years. My well in North Texas is 1 HP wit 1" 1/4" going to the house. Should you put the tank closer to th3e house, or maybe use a booster across that 100 ft.
Not a pro but an engineer