A few questions:
* Is the well a screened well (casing to a screen) or is it open bore (casing to rock then a hole drilled through the rock)
** If the well is screened how long is the screen?
** If the well is an open bore how long is the casing?
* What depth is the pump hung at? (how far below the surface is the pump)
* Can you provide more details on the failed casing? Did the driller send an inspection camera down and tell you it was breached at XX feet?
* What state are you in? There is significant differences in well construction by state. For example in Valveman's area (Lubbock TX) I doubt they require underground discharge at 6' or more like they do in MN.
Without knowing all the details I am going to make the assumption that the casing is not breached. If the casing is breached then your going to need to get a new well. Not all drillers are good at fishing. (a fish is what is stuck in the well you want out) Fishing requires lots of different tools then drilling, and different skills. Valveman has hit the nail on the head.
There is not much room between a 3.75" pump and 4" steel casing.
Call a few well companies and see what they say, if one gives you a name of who they believe is the best fisher then go with them. A competent well company that knows how to fish will have a good assortment of tools to get the job done.
Maybe it is because I talk to so many people who are trying to DIY after they have been taken in some way or another by a so called "professional pump installer". But I also sell to a lot of real professional pump installers, and you are correct, good ones do exist.
It is challenging to sort out a good from a bad driller. That is why I like to talk to several, and if one driller recommends another you know they have to be good. (guy I worked for did not even have signs on the side of his truck because he had too much business, all of them recommendations)
First thing they will do is try to clean the pump off using water and / or air. Then they will start working the pump free. 1" galvanized pipe is the best thing you can ask for when dealing with a stuck pump in my opinion. You can work it up and down, to clear obstructions. Try pushing on an aircraft cable. Also if the galvanized pipe breaks it is easy to get an overshot to set on it to resume the pull. If you break the pump head off a nice pointy taper tap will go right through the motor and pull it out.
Once the pump is out you need to fix the problem on how well is getting sediment. If it is an open bore then it just needs cleaned out. If it is a screened well then the screen most likely needs replaced.
For a new well, I like an PVC casing with galvanized drop pipe, in some situations a metal casing can be better, and the driller will advise. But that is my opinion. Galvanized is easier to fish and hold the pump more stable, PVC never rusts out and is more affordable, neither is wrong, both have their place and there is a strong personal preference.
PVC drop pipe is a better choice.
Don't install a safety cable of any description. I have never rescued a pump because of one, but have lost some.
2 wire motors last for a decade, 3 wire motors last for decades.
Family business now for 87 years, been doing it since I was 7.
Safety cables are a pain to deal with when they break and coil up around the top of the pump. It makes retrieving the pump much harder.
The driller will determine if the well is an open bore or screened well, how deep to drill, what size screen if needed or how deep to set the casing. This varies by region, and what works in one area will not work in others. I know where I was working a quarter mile could make a significant difference in what attributes a good well needed. If it is a screened well I would go with a stainless screen held in by a k-packer. I abhor slotted casing. I would use a 3 wire pump as others have mentioned.
I would also go with a spool type of underground discharge such as the ones shown on page 6. They are easy to get to seal, limit what can fall into the well, and rarely stick.
Next best is the V notch type. They are bit more of a pain to set and if junk falls into one once you have removed the drop pipe can make it hard to get one to seal. They also take up room in the casing.
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I hate snappy's. I cause bodily harm to the person who invented them if we ever met. The pain they have caused me. (actually they have made me a ton of money. Get to sell the customer a new underground discharge and charge for the backhoe to dig the old one out after they freeze up and the aircraft cable snaps) We had several special tools to try to free them up, but sometimes they would win and we had to get the backhoe. They are the worst to tell if they are set correctly and will drop without warning if not properly seated.
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I agree with Valveman and am not sold on VFD pumps for normal usage. In certain situations they make sense such as cabins where a pressure tank is one more thing you have to drain prior to winter.
The installers are also being lied to as the manufacturers are pushing VFD's because they also make a lot more money than on a normal pump system. Saying a VFD saves energy or makes pumps last longer is just not true. But they say it over and over until people believe it and spend several times more on their pump system than they should.
The guy I worked with did mostly fishing. It was not uncommon to have to retrieve another company's tools they lost before we could start pulling the pump. Minnesota had a law that if a house sold all wells had to be functioning or they had to be pulled and sealed, health department was adamant we get everything out but the screen. Many of the wells had not been functioning since the 60's. Dirt on a pump was a normal situation, as was drilling out cemented in wells that lacked proper paperwork. Your well assuming no breached casing sounds like standard work.