I know that most of this has been about vet experience, but as far as animal experience goes, I would highly recommend research (if you're an undergrad, I know it is far more difficult to get in with a job like this for non-tradit.).
Not all research will qualify as animal experience though—so be careful if that is your aim—but research in general always looks fantastic on a resume (animal related or not). It's going to be like any job, you have to work your way up and in, but you can get some really valuable hours this way.
I started undergrad with no production animal experience and left with hundreds of hours because I worked in a lab that works with birds, cattle, and pigs. After a year, I got to know the people in my lab pretty well and I did my own research project that I get to present at a national convention (ASAS Midwest Meetings 2012!!). Personally, this had a huge impact because I'm planning on going into production animal medicine now 🙂
I was also able to pick up some pretty valuable hours during one summer because I was a field research tech—I got to learn small bird handling. Summer research projects can be fantastic if you're looking to have a job and get what may end up being a unique experience.
My two cents about vet experience—If you can get a tech job, more power to you. I would have loved that opportunity, but during the school year I wouldn't have time, and summers are always up in the air for me (I'm OOS, so if I wanted to stay, I had to find a job, which didn't always happen). I personally was hell bent on getting large animal clinical hours. Honestly, there just aren't that many out there and they definitely aren't hiring. I spent hours calling clinics (large, small, mixed) and many were unwilling or unable to even give me shadowing time. I found the best way to go about simply finding someone to get time with was to look up as many as you could, and when a clinic tells you no, ask if they know of other clinics in the area.
The best you can do is really just chip away at the hours a little at a time, in any way you can get them.
Good luck!