Time and Money...our biggest challenges!
Do you have a google account? The video could be very easy for you if you dowload Google's Picasa program for photographs. It's FREE! There is a feature where you can select the photos and the music and it will arrange it into a movie for you.
Another option is Windows Movie Maker. Again, usually FREE on your computer, and you can import photos, music and make a movie. Depending on what all you do to it, transitions between photos, captions, length, etc. you could do a short video in an afternoon. You could also have the video playing in the background of the party.
There are many free sites for royalty free music out there too.
Here's a link to one I did for my son's birth with Window's Movie Maker: http://heathers4.googlepages.com/memorymovies
I know the cups would be "easier" but I've made a few videos as 1st birthday gifts for my neices and cousins and they've been a very treasured gift to the grandparents, and parents of all.
Other ideas would be a photograph for a thank-you note. I have a Send Out Cards account which I LOVE and I use it to send out personalized cards to family members thanking them or just staying in touch.
How neat for Grandma in AZ to get a photograph of my son playing with his toy barn she got him as his thank you note. Took about 2 minutes total (including upload time for the photograph) and she has a picture to enjoy of him playing with the barn.
You could do one of your daughter eating her birthday cake, or opening her gifts or somehting and send a personalized card to everyone on your guest list all at once. That could be a huge time saver for you post party! People rave about these cards when they get them, and I usually get a phone call thanking me for the thank you card. LOL
You are welcome to send a card for free to try it out: www.sendoutcards.com/25194 and I'd be happy to answer any questions you have.
Oh, one more suggestion about a favor, candy bar wrappers. Measure a hershey bar and design a fun wrapper with your daughter's photo on it, and a Happy Birthday. In the ingredient section list sweet smiles, wet kisses, first words, etc. that make up a 1st birthday. I've done these for my older girls and they're so cute! Everyone raves about them too. You just wrap the 'new' wrapper over the candy bar and glue it with a glue-stick. It's pretty inexpensive too. ;)
Good luck and enjoy your celebration! H.