I am assuming from your description that you have a submersible pump in the well. If your pump is above ground, then come back and tell us what it is.
This reply suggests some things you would need to do if you are not 100% certain that the problem is the pump. I am including this because it is often concluded that the pump is bad when something else, such as a leaking pipe in the well, is causing the problem.
The pump is often not set to the depth of the well. The water may come up nearer the surface. Therefore, the pump may not be 350 ft down in the well.
What are the symptoms that cause you to believe that you need a new pump? That is the first thing to deal with because a wrong conclusion will be very expensive.
You should somehow find the characteristics of the pump in the well. It could be from 1/2 to 1 1/-2 horsepower, and there is a wide range of pressure characteristics depending on how far down it is to water in your well.
If the pump must be replaced you probably need to match the horsepower and pump characteristics, unless you find that it is not a good match for your well and system.
Whether you could pull the pump without special equipment depends on what kind of pipe is running from the pump to the top of the well. If it is a soft balck plastic (polyethylene - often called "poly pipe") and it is not too large and not too deep, it may be possible to pull it without special equipment. If it is rigid pipe such as PVC or steel, it will probably require special equipment.
Until you know what your existing pump is, you can't know the cost of a new pump. Depending on horsepower and characteristics of your existing pump, a new pump that you buy yourself might cost in the range of $400 to $1000. If you pay retail it could cost $600 to $1500 for the same pump.
Installation of a new pump could add more than $1000 to that if the pump is set deep in the well. You will probably not be able to get firm quotes from anyone unless they know what is in the well, or any firm quote you get will have a high price to cover the unknowns.
So your first steps should be:
1. Determine exactly what is wrong with your system.
2. Determine the HP and other characteristics of your pump.
3. Determine if you could fix or replace it yourself.
4. Get prices on pumps.
5. Then decide how you want to go about getting your system fixed.
If you hire a well and pump company to fix the problem, they should try to diagnose the problem before pulling the pump, pull the pump, determine the model so they can select a replacement, replace the pump, pipe, and wiring, and get the system working. If it is a normal jpb, it could be done in one day. It would not surprise me if the bill is in the range of $1000 to $3000 depending on depth and size of pump.
If it is not an emergency, you have time to do some things that could save you some money.