All of this can be researched via Google.
I just typed in one of your questions (cost to fly from NorCal to Tanzania) into the old googles and boom information like fucking magic.
Look man, no one knows what you and your mom like better than you (and your mom). Write down how you think the trip should go, what you need to accomplish it then start pricing shit out. You're not going to know the flight costs exactly right now if you're looking at taking the trip in a few years, but airfare has been fairly stable for the past few years and shouldn't fluctuate too much between now and then.
Read reviews by people who have gone on a safari in both Kenya and Tanzania and possibly other countries around there (that are stable). Research where they went, who they went through, where they stayed and figure out the costs from there. Does it fit in your budget? Can you save enough over "n" years to afford to go?
As far as personal safari experience, I've never flown to Africa, but my wife and I planned a trip to India (Mumbai and Goa) and that was interesting. Check into whether you need any special type of visa to get into either of those countries, what the process is attaining said visa and how long the visa is valid for then start planning backwards giving yourself a good window so you'll definitely get it (if applicable) and it won't expire until you're safely back in home.
Also, research immunizations before heading over there - you'll probably need typhoid and a malaria medication, figure out it your insurance covers the shots, if not, how much they cost? Every time I've traveled abroad, I'd contact my local pharmacy to see how much the shots I'd need costs and their availability.
If you and your mom don't have valid passports, get the ball rolling on that, too. You'll need the passport before you can start the visa process (if applicable).
There's stuff you can start doing now to make sure you can get there when you want to get there...