Is car detailing worth it?

My cousin gifted me her old car at the beginning of the year. It's it good shape, runs fine, and the outside is clean (no dents, scratches, rust) but the inside is a different story. It's disgusting. There's mysterious stains on the interior, stuff crusted up in just about every crevice there is, dog hair everywhere... you get the picture.

I'm totally willing to pay a professional to do the job right. My dad on the other hand thinks he and I could just go to the car wash on a nice day and do it ourselves. Personally I think going to the car wash would be impractical. The amount of quarters it would take to properly vacuum out the car completely would probably be close to equal the cost to hire someone, plus that wouldn't be taking care of the dirt and stains.

I've never had a car detailed before so I don't know, maybe it's frivolous.
Any advice? How much is a good price to have a car professionally cleaned?
Is car detailing worth it?
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