Basketball is pretty much 90% of my paid work at the moment.. and from April to October.. about 99%...
There are as many different lenses you could use, as there are different actions you'd think to photograph (of course the BBL venues aren't the biggest in the world.. so the longest ones not much use in domestic games - apart from Cup/Trophy/PlayOff Final).
The widest I use for basketball photography is 10mm - and the longest I use is 600mm.
So you can take your pick from that range.. and each lens gives you different view/framing of the action.
The 'go-to' lens if you only work with one body, it would be the 70-200mm f2.8 - you are pretty good to go with that one and will get a decent variety of images with it.
When ever someone asks me which lens they should take when going to their first basketball games to photograph.. it's the 70-200 every time
Depending on the venues, and access to photo positions.. then it comes personal choice (or customers requirements) ... many do like the 24-70 as their second lens.
And if you are doing a game where you need to be behind the advertising boards.. then 24-70 would be a good second choice, as you aren't getting any low angles.
My personal second handheld lens choice quite often goes to Samyang 14mm ... super sharp and great for those low angle images from next to the hoop. (check access with clubs - and also in smaller venues the ceiling/seating isn't that 'spectacular' ..)
Or otherwise the Canon 16-35mm .. but really do like the Samyang 14mm..
Then for remotes .. ceiling ones often on the 200mm range.. behind the board anything that gets you close to 18mm / 22mm ..
For the close up images of player.. 300mm/400mm (or I use Canon 200mm-400mm with the x1.4 built-in..)
BBL is a 'easy' league to get to photograph and has seen an explosion of photographers in the past two seasons... it used to be just handful of photographers in the whole league.. now it's sometimes 10 photographer in the game (London Lions are getting really popular with the photographers).
If you can find your own little 'market' .. there is some money to be made from the game (yes, even in the UK!!) .. but as with sports photography so often.. what matters the most is that you 'know' the right contacts.
It is definitely a sport that I would recommend for anyone to give a try .. and after doing basketball for a long time.. every time I get to a football game, I am surprised how slow and predictable football is in comparison to basketball ;-)
The nice thing about basketball is also that with the 70-200.. you are able to cover the game all the time, at both ends of the court (yes, bit of compromise when photographing the other end.. but very doable!!).
So there is no time when you need to wait for the action to come your way .. it's full on photography for the whole game!!
You should be well equipped with the camera body you have at the moment, and the 70-200 is a great way to get into basketball photography.
Also, mostly the photographers in basketball are a friendly bunch.. they are happy to talk to you before a game and give advice the 'newbies' .. so head to your first game early and have a chat with the photographers.
As for the usage of the images from BBL games.. not 100% sure what the agreement reads out.. but I keep on seeing tons of images on FB galleries, blog posts, Instagram, Twitter..
Maybe drop the guys at BBL a quick message (should get a reply from the same guys who you mail the 'agreement' to) .. helpful bunch at the BBL offices as well.
Not sure there is much that makes sense in my long blabbering on about the sport i love to photograph.. but hopefully you have picked up something useful from there....