You need to decide exactly (or exactly as possible!) WHICH museums you want to visit.
If you think you will have time only for the Museumsinsel museums, the Welcome Card + Museum Island, which also covers full use of the entire public transport system, may be your best option (but see below, re your location and what I think may be your limited use of public transport given that you'll be within walking distance of the Museumsinsel museums).
If you want to visit more of the state museums - for example, the Gemaldegalerie and the Kupferstichkabinett in the Kulturforum, the Dahlem museums, or the Charlottenburg museums - the three day, 19-euro Museum pass will be the best. You will then need to buy single or day tickets for your public transport use.
You've got to do the sums. As your main interest is the museums, you're unlikely to use many of the discounts that might make the Welcome Card worthwhile (but see below re the museums NOT covered by the Museum Pass).
The Berlincard is new, and seems quite expensive.
If you're planning to visit all the museums on the Museumsinsel in four days and are staying near Bahnhof Friedrichstrasse, and if you're both reasonably mobile, you'll be able to walk to all of them and may not be making much use of public transport, so the Welcome Card stops looking like an option.
On my first couple of visits to Berlin I spent almost all my time in the museums and hardly used public transport at all, so the Museum Pass was my best option. (I got the annual pass for 40 euros, which pays for itself in 4-5 museum visits: that might even be an option for you, if you're likely to make that many visits in four days.) For museum-goers, the Museum Pass is terrific value.
Note, though, that it covers "only" the State museums, not the private museums like the DDR Museum, or the Deutsches Historical Museum. Or, alas, the Berlische Galerie or the Bauhaus Archiv - but the Welcome Card gives discounts on these. If you went to both, it would save you 4 euros on the 8-euro admission to the Berlinische Galerie (50% discount) and 2 euros on the Bauhaus Archiv (30% discount on the 6-euro admission). However, given the time you are going to be spending on the Museumsinsel, you could be paying for a lot of public transport that you wouldn't be needing.
It IS confusing, I know, but in the end it boils down to what YOU want to do and see, so I'll finish as I began, and say that you need to decide which museums you'll be visiting, and how much you're likely to use public transport.
I'll take a guess, I think it might be most economical to buy the 19-euro three-day Museum Pass, and pay full price for your entries to the Bauhaus Archiv and the Berlinische Galerie, and buy tickets for what will likely be ad hoc transport use.This is what I would do.
A final point (yes, another wrinkle to consider) about the Welcome Card: if you are planning visits to the theatre, opera, or concerts, which really do yield big savings, it is definitely worthwhile. But your dad may be too tired after all those museums to want to step out in the evening :-)
And really finally, there are no discounts for seniors! I'm sorry this turned out to be so long, but I hope it is helpful.
Edited: 2:42 am, June 20, 2012