Need help choosing rims for fixed gear
As @Batman said in a comment, the main thing is to get the spoke count right. So count how many spokes each wheel has (they could be different). Next, measure the width of the rim. You'll need to take the tires off first. And look at the tires to see what dimensions they say they are.

Next, you'll need to make some tentative decisions. I recommend keeping things as they were, unless you have a good reason to change. Do you want similar width rims, or wider / narrower? Do you want deeper profile rims? Do you want to use a similar lacing pattern? Are you going cheap or $$$?

Now take the mangled wheel(s) to your Local Bike Shop and see what rims they have that match your criteria. Get them to double check your spoke count, and to recommend what length spokes you need.

Finally, since you mention getting rims and spokes, who is going to build these wheels? Building them yourself is not hard, but it can be a slow job if you haven't done it before. Most people just pay an expert.