15" rear tyre change options

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Now I've installed the new shocks I need some new tyres so I can get the car set up properly. What was the net result of this lot above me? I have, I think 11" rear rims and again I think 7" front rims. I say 'think' as the tyres are still on and can't get an accurate measure. The current Pirelli 345s on the rear are too wide. I'll be doing some track days but the main use will be on the road. Mel did show me some of the tyres he had but as Vince has said earlier, the tread was very shallow and I would like more than that ideally. Of course I want to get them as competitively priced as possible. Any suggestions as to type and where to get them from? Thanks in advance.

ps Currently have 225/50 R15 on the front and 345/35 ZR15 on the rear.