If you are confident that you will both enjoy the more complex all-day version from the start off then 1941 is probably now redundant for you. But if you want an evening version which is easier to learn, then 1941 is just the ticket.
Many of us began the journey towards owning multiple versions of A&A by thinking about how to top up the pieces in the box of our first version. But as an owner of Anniversary you might top up your pieces by purchasing something other than 1941 if the more complicated versions are your thing.
I certainly played solo to learn the game and know that others did so too, although playing yourself is likely to become boring very quickly.
Alternatively you can play on the computer using “triple a” software available via this forum. If that is what you want to do, then one of us will be very happy to point you at the instructions, etc.