I'm learning about asparagus myself. I planted it last year and this year as it comes back I pick a few and let a few become the big ferns. I've been keeping other plants out of the asparagus - I want this crop to return successfully every year so I'm not letting other stuff compete with it. Not sure what people who know what they're doing with it would suggest. Perhaps someone else will answer.
There are various repellant products that you might be able to use in the garden to keep animals away. Your best bet is to visit the Natural Organic Library
and look up each of the animals you might have to repel. Birds are a real problem in my garden, they attack the strawberries and some of the tomatoes. My solution was to not put up bird feeders this winter (it was very mild anyway) so they weren't habituated to coming to my yard to eat.
If you have some discarded CDs at your place you might want to hang some with monofilament so they twist and sparkle in the garden. That might discourage exploration to begin with. (It's what I need to do also.)