We have hauled all ours in our Taurus station wagon. We just drop the back seat, put packing blankets we keep for just that purpose down, and in they go.
We use something very similar to Sheepgirl. Depending on the weather and the distance of the drive, We put plywood on the top and 3 of the sides for wind and rain protection. We don't travel in the winter to pick up new animals.
We've hauled more goats home in a truck topper than you could shake a stick at. It's our 'preferred' method. We have a trailer but...unless it's a HUGE buck we don't want to lift, the truck is easier.
I brought my two kids home in a large dog crate in the back of my '89 olds. I think I'm going to use the truck though with the two does I'm getting next month.
DD brought her Lamancha doeling home in the back seat of my hubby's truck. (Shhhhh.) It was only a 10 minute ride and no messes. She was nice and calm since she was a bit scared. Our wether was from next door, so we walked him home.
For the health certificates and to go to the fair we put them in the XX lg metal dog cage with a rubber mat in the tray in the back of my Expedition with 2/3 of the back seats folded down. It fits perfect. Its not far away, though, so it works. I don't think I'd want them in there for hours because it would likely get smelly. We will probably eventually make a "top" for our 4x6 trailer so we can use it for goats, but we don't need to till after we have babies.
The kids are still 'small' (between 80-130#) now but if we need to move all of them at once, the truck bed would be too small. We are considering getting a 5'x8' or 10' cargo trailer with windows to haul them around. I really don't care to haul them anywhere...seem like every time I did that, they got sick! We do need something...in case of emergency...which we almost did when we had that big fire.... Yeah, hauling them in car/truck is so much easier...
I use a dog crate in the back of my crossover. Last one I got was too wide to fit thru the door. So, we had to make her "suck it in". She is a thick girl. Luckily it was only about a five mile trip.
We used a dog crate in the back of our Suzuki Grand Vitara. Last goat we got was a touch tall for it, but the trip wasn't but about 10 minutes so it wasn't a big deal. We need a bigger dog crate for adults. When we got our first 2 they were 5week old kids so both fit nicely in the crate together with room to move if they wanted to.
Put them in the "trunk" of my Toyota Sienna minivan. I can fit 2 smaller does back there together. It's a big deep trunk space, the back bench can fold down into it.