there is bike and bike+ - what's the difference?
Bike+ has a bigger screen, the screen tilts and turns around, and it has electronically controlled resistance so you never need to recalibrate the resistance, which is a known issue on the Bike model. I went for Bike+ because I wanted the most future proof option available to me at the time.
do you have to buy shoes etc in addition?
Yes you need shoes that are compatible with cycling cleats. You can buy as an accessory or you can buy any cycling shoes which fit Look Delta brand cleats from any cycling shop. Peloton branded accessories are overpriced imo.
How does the £39 membership work - do you also have yoga classes etc on that? Are they any good?!
There are hundreds of classes to choose from across multiple disciplines. Cycling, strength, yoga, pilates, stretching, bootcamp, outdoor walks/runs. Choice will never be a problem. There are lots of online community groups that set up events throughout the year too. I enjoy this aspect a lot.
how does the £39 membership differ from the £12.99?!
£12.99 is for the app only. Lots of people buy a cheap gym style spin bike and use the app only. You don't get any ride data (speed/cadence/power etc) without the £39 option so if you want a Peloton bike you need to be OK with the £39 too.
are there ever any discounts I should be aware of?
Yes there are discounts around 3x a year offering a few hundred pounds off.
I'd suggest you sign up for the app for a few months to test it out and then when the bike is on offer you'll know if you want it or not.