If you don’t care what show you can get tickets to, check out the TKTS booth in Leicester Square. If you want to try to get discount tickets ahead of time, there are websites with discount codes. You have to get a login for the website, but it is free.
Is it worth buying them from the booths in piccadilly or the internet? I want good ones like a good view of the stage.
The best website for finding package theatre ticket and hotel deals is http://usefulwiki.com/londontheatre. They also offer packages with restaurants if you are interested. I would go to the site and see what the options are for your preferred show/hotel location.
If this option is out of your budget, book a cheap London hotel or B&B and once you get to London visit the TKTS booth in Leicester Square for discounted tickets to that night's shows. This is really only a good idea if you don't have a preference what show you see since the tickets sold by TKTS are for shows with seats left for that night's performance and they do not offer tickets to new shows. The booth is open Monday – Saturday 10:00-19:00 and Sunday – 12 noon to 15.00. For the best chance of getting tickets to a good show, get to the booth a little bit before they open. TKTS is completely respectable and your tickets will be legitimate. If you buy discount tickets from one of the many shops in London that offer them, your tickets will likely not be legitimate. You can find out more about the location of the TKTS booth and how it works there. Cheers!