I am gonna start undergrad this year hopefully so I can only speak for the undergrad 1st year options (they are bankside, high holborn, roseberry, passfield, carr saunders and northumberland), if you want your own/shared between a few kitchen that that will be High Holborn, the other's have shared fridges and stuff but you are sharing with a whole floor. Bankside has some kitchens to but from what I have heard not everyone get's them and their are waiting lists.
For an en-suite your only option is bankside, you either get your own toilet or you share with one other person. The rest don't have en-suites but according to my research the highest toilet : people ratio's are at HH, RB/CS and I haven;t done any research on the other two after I found that 1st year undergrads must share rooms.
All of them are withing 25 mins to LSE as they are of course LSE halls, the closest being HH I think.