What components need to be changed when upgrading from R22 to R410a?
On the AC side everything really needs to be changed R22 uses mineral oil based lubricants. 
R410a uses ester oil lubricants. Getting all the residue out would cost a bunch and these can’t be mixed.
The compressor will need to be changed and the TXV / orifice will need to be changed.
You might be able to have the evaporator cleaned (indoor coil) if it is in good shape and the size will work.
Most of the time the older outdoor coils are in rough shape and of older less energy efficient design. Cleaning and changing the parts are not cost effective.
It would help to have the model because some units have adjacent coils and some the coils are interlinked for improved efficiency. I have only worked on a couple of old units but they just needed a recharge, I know some charge $100/LB for R22 but it can still be purchased if the system is working.

Just an update, another Stack exchange member posted there system had been upgraded and now is not working well from under sized lines and possibly contaminated oil. Just thought I would add this to help your decision.