Code says the minimum amps for a new service panel is 200amps so I would go with the electrician’s recommendation there. This is in spite of the fact that you’ll never really use 200A.
If your three plug outlets do not have a ground then they are unsafe if you have a short with a three prong plug in them. Changing to two prong isn’t going to help though. If you want to plug in a three prong to a two prong outlet you’ll get a converter and then you have the same problem again.
I looked over service panels while picking up some supplies I needed. I was surprised. A 20 slot, 100amp panel was $49 while a 40 slot, 200 amp panel was $130. Still, $80 won’t buy you much labor these days. Very many larger electrical appliances eat up slots fast. I have a stove, pump, drier, backfeed, A/C, and whole house surge protector wolfing up over half my slots. No wonder I had to give up 2 more for a sub panel breaker.
Oh, the back feed breaker has an approved interlock insuring it and the main can’t both be on at the same time.
As others have said, since you are doing it anyways, do it right.
In the 1940s, electricity was primarily used for lighting, which draws very little power. Today, we have central air and heat, dishwashers, and whole bunch of toys which draw a lot of power. Even if you aren’t getting the new kitchen, pool, spa, etc. today, at least have the electricity to where it can be done in the future. I would also recommend upgrading the 2 prong to 3 prong for the same reason.
When you HAVE to plug in that brand new HDTV and the only wall socket that is available is the 2 prong, you WILL chop off that fat bastard plug or defeat it some other way, leading to very bad things…
A lot of your electronics have 2 prong plugs. However, to give you full protection, surge protectors need a sound ground. You don’t want the first lighting storm to fry your HDTV.