How much can I do on my own (adding breakers and rewiring?
Looking online a home owner can do there own electrical start to finish.
If you want to work with an electrician and find one willing to let you pull wire and connect devices ahead of time the electrician will want to inspect it and if you wire the receptacles he will also want to look as well as an inspector will to verify there is 1/4” of the cable covering on nmb extending inside the box and 6” of wire and of corse properly wired at the receptacles, switches snd lights.
When you pull to the panel location since it is new bring your wires in and make sure there is enough to reach any point in the panel. For example when I wire panels if I enter on the left I land the ground neutral and hot on the right yes this consumes wire but when balancing panels once powered up I never have to splice and later remodels I always have enough wire. Other electricians won’t waste a 1/4” of wire so knowing what he wants is important.
You will probably want a service upgrade also most homes on fuses only have 60 amp sometimes 100 amp services I would suggest while you are at it go big and not only increase the service size but get as many breaker positions as you can.
The minimum panel size for a single family residential job is currently 100 amps.
The advantage of working with an electrician is he will know what is allowed and can advise of you in some cases saving quite a chunk of $. Also in my jurisdiction we have one inspector that must hate home owners and makes them do more than required by code. Make sure to mention it was wired by an electrician(s) and the inspection may go much faster.
When I moved to my current home it was in a jurisdiction I had not worked in often and my first job was similar to yours updating a 1930’s farm house with a new service.
The inspector was not going to sine off the job with multiple “violations” I asked him to cite the code references while getting a code book. After giving him my license number he started backpedaling big time saying that’s how he liked it and approved the permit with a green tag on the service.