Hi J.,
We were forced to move to a Big Boy Bed when my little one was 22 months old. He climbed out of the pack and play at Grandma's over Christmas and when we returned home, we just decided to make the transition. We bought a toddler bed at Walmart for $50 and just continued to use the crib mattress. My little guy is in the 80th percentile for height, but this little bed will be plenty big for him for quite some time. We like it because it is close to the floor, so he can climb in and out with ease. He's only fallen out once, but it was not too traumatic, since he was already so close to the floor. It's also nice for us because he has a small room, so the little bed doesn't take up as much room as a twin bed will. If you already have a twin bed, you can just buy the rails to attach. If not, a toddler bed is a nice "in-between" and none too expensive.
As far as getting them to use it, it just takes time! We were lucky with my little guy - he just stayed in there from the get go. Even at Grandma's! While he does occasionally climb out to play with toys at naptime (and there are TONS of toys in his room), I simply put him back in bed and tell him night night, and he almost always complies. I think I've only had to do this three times at the most. You just have to be consistent and they'll get the hang of it.
Best of luck with your new Big Girl!!!
Amy K