What tools will I need to remove sprocket/what type will I need to order? I have a flip-flop hub on a single speed track bike.
I need to replace the rear sprocket (freewheel side) and chain.

Id prefer to give this a go myself, but 


Not sure what tools I need to remove this  
Not sure what freewheel I would need to order to replace it with.
(ideally a similar or upgrade.  + points for links to sites like Evans/ChainReactionCycles)
That will be a BMX freewheel tool you will be needing. Order a BMX style freewheel, count the teeth or get one with less/more teeth depending on how you want to be pedalling - higher cadence will need more teeth.

If you have access to a big vice then you can put the freewheel removal tool in that. Otherwise a really big adjustable spanner from some pound-shop will do nicely.