I guess you'll be flying into Manchester Tode? And if it's for work, Im sure transfers to the North yorkshire are included, so no need to worry about the long tube ride.
Only get an Oyster if you've going to be in London more than 2 days, it was a 10 pound deposit last time I went to get one. It's handy being able to tag on and off, but if you're only gonna be on the tube a couple of times, its not really worth the hassle of getting the card and then getting the deposit back.
If you're looking to head to some shops, Regent Street and Oxford Street are good in the city, or the Westfield London mall in Shepherds Bush is huuuuuge.

www.thetrainline.com is a good place to look for all of your domestic train tickets. I found that I saved a fair bit of money, especially for trips between Liverpool\Chester\Manchester and London on Virgin Trains.