Thank you all for the input and advice.
MikeBear - I have added receptacles, recessed lights, and two bathroom fans. Clearly, replacing the panel is another ball game, which is why I asked. It is legal for the homeowner to do this work. The panel can be upgraded without having to change anything in the house. But as I move forward in remodeling the kitchen or adding a bathroom, then of course those would need to be brought up to code with AFCI breakers, GFCI around water, grounded receptacles, etc. I can't make those upgrades, though, until the panel is upgraded first.
Greg - Thanks for the input on various details.
CDP45 - I view this as much more than a financial forum. I am reading through other forums on diy, electrical, plumbing, youtube, and so on. But I thought this forum would give me a different perspective, with less naysayers and more help. And it has!
SkunkFunk - Unfortunately, that's what I'm thinking about - how can I hire an electrician do the most complex work, while I take care of the tedious, time consuming, repetitive or simple tasks to save money and learn new skills?
To everyone - thank you for your comments. I see there is no general agreement about whether I should/could do the work, other than I should literally NOT touch anything from the power lines to the house. I'm meeting with some electricians this week to get price estimates and will talk with each of them about what tasks I could do myself. I'll keep you posted on what I decided to do.