I'm not a big fan of plays but can highly recommended some musicals.
A lot depends on your age and interests - Mamma Mia is a real "girlie" happy-go-lucky musical. Wicked is fantastic as is Hairspray! All easy to watch and an enjoyable night out for everybody, even those that claim they don't like musicals.
The only play I have been to see in the West End is The Woman in Black which I enjoyed but imo you can't beat a good musical.
Whether or not you need o pre-book is dependant on a lot of things. Is it during the week? Is it the weekend? Is it a popular show? In general, I would recommend pre-booking tickets if you are going at the weekend and if there is something in particular you really want to see. If your easy going enough you could leave it till you get there. I would also recommend that you book directly with the theatre as you will get better seats.
We travel to London approx twice a year and try to fit in as many shows as possible so enjoy!