A museumjaarkaart costs €35 pp, no discounts for seniors. It is not valid in the Anne Frankhuis, but is for the others you mention. You buy it at the first museum you visit. It does not include public transport, but strippenkaarten are cheap and easy to use, and it is easy to buy train tickets too.
The iamsterdam card again doesn't include the Anne Frankhuis, but does include public transport within Amsterdam (so not to or in Haarlem) and offers discounts on other attractions with in Amsterdam. For a 72 hour pass it costs €58.

Personally I would go for the museum pass if you are going to be in Amsterdam for 7 days. You can then buy strippenkaarten for the trams and buses.
Buy your tickets for the Anne Frankhuis online to save having to queue. Choose either an early morning or a late afternoon/evening timeslot to miss the worst of the crowds there, which greatly detract from the experience..

definitely buy the Anne Frank tikets on line. Having those in hand will help you avoid waiting in ANY lines except the few folks who have picked the same time you did....believe me, the line of people who DIDN'T buy tickets ahead will almost undoubtedly stretch around the corner.

definitely go for the museum card, valid for one year €35 + administration cost. The card is not only valid for Amsterdam museums, also for museums all over the Netherlands.

If you have time include Mauritshuis http://www.mauritshuis.nl in The Hague
and Frans Hals Museum http://www.franshalsmuseum.nl/in Haarlem.

Here is a list of Museums in Amsterdam which honour the Museum Card
http://theamsterdamguide.planeteye.com/museum-card/

Thanks for your replies. I was leaning toward the museum card which looked like a better buy for me, but was doubting that because of all the advertising for the iamsterdam card that I have been seeing. We will definitely go for the museum card.

I also have some questions about the train from the airport to the city. (forgot to post it yesterday)
We are arriving at about 8:30 AM and staying at the Hotel Pulitzer. I thought we would take the train into Amsterdam then a taxi to the hotel. Is that smart? Is the train as user friendly as the Heathrow Express in London? Any tips about the train ride/tickets/taxi to hotel?

Thanks

I have taken the train into the city from the airport a few times. It is simple. Take a cab from central station to hotel if you think it is too far to walk. Easy as 1 2 3..

Connexion has a hotel shuttle from Schiphol which serves teh Pulitzer.
http://www.schipholhotelshuttle.nl/site/toonhotel.asp

If you decide to go by train and taxi then make sure the taxi is a licensed cab. It must have blue number plates. If you can use one which has TCA on it rather than a not affiliated taxi, as these are less likely to rip you off. Taxis in Amsterdam have a bad reputation, and are expensive, so only use one to and from the hotel not to get around the city.
If you don't have much luggage it isn't that long a walk. Or get a bus (the 170, or 172) to Westermarkt and it's only 3 minutes from there. Trams 13 and 17 also stop nearby. The stop/go bus also goes along the Prinsengracht and will stop b your hotel if you ask the driver.

And if taking the airport train be sure to get on the right train - about half the trains 'to Amsterdam' do not go to Amsterdam Centraal, the main downtown station but about half or so go to Amsterdam Zuid-WTC or RAI and not to Centraal Station - both trains use the same platform so be sure to look at the overhead monniker trackside to see if the train is going to 'Amsterdam C.S.' and not Amsterdam Zuid or Amsterdam RAI

I often see people who have gotten on the Zuid or RAI trains and thought they were going to Amsterdam C.S.

Is the train as user friendly as the Heathrow Express in London? Any tips about the train ride/tickets/taxi to hotel?

Yes, just as user friendly, much cheaper, and not as fancy.

Beware of pickpockets and luggage thieves on the train and in and around Centraal station. Hang on to your bags, especially the small bags, and go on red alert if you are bumped or see an unusual distraction. There is often a platoon of Amsterdam cops watching everybody entering Centraal station. Have some euro cash on hand for the taxi and pay attention to the advice of hetismij. The taxi rank is right outside the door of the station.

Per Dukey, I've walked past the Anne Frank Huis several times in the past year and the line is always at least 50 yards long.

The hotel bus from Schiphol is easier though - it drops you at your hotel door.

If you do not book Anne Frank House ducats online check the VVV (Amsterdam Tourist Office)which in past years at least, were advertising on their window they did such reservations. I saw this on the VVV by the Leidesplein two years ago.

If you have a museum pass, do you get to skip the line like the folks who have a pre-paid single ticket?