I need to run the cable from the existing power source 245 feet to the pedestal beside my RV.. What size electrical wiring and conduit do I need to purchase? I hope to trench and lay the conduit and have an electrician make the connections.

The RV requires 50 amp service.
I also want to tie n my shallow well pump to 110 V.

Well, there is far more to it than just laying the conduit and making the connections. In fact, making the connections is the simple part, it takes a lot more knowledge to install the conduit, set the boxes and pull the wire.

245' is a long way to go, so we'd need to know a bit about the well pump other than it's 120V and a shallow well. What motor is it? Where is the pressure tank?

For a reasonable load from the RV, like 30A or so @ 240v, you'd need #4cu or #3al. Then adding the well load will change that to larger wire if the well is fed from the same line. If the tank is not at this area you need to come from where the tank is and that will require a separate feed to the well.

Suffice to say, there is not enough information right now for an accurate answer.