To be a record signing it'd have to be someone 22-28 years old imo. Younger or older and it's much riskier imo. So from a quick look at Barca's wiki 5 candidates jump out.
Neymar 24 ....think he'd be fantastic for us (probably best return on investment) but can't see Barca selling him.
Alba 27 ......don't we have a history of record fees for full backs :-) .... but this is supposed to be a British record for any position so I doubt this one.
Busquets 27 ....along with Fenandinho and Gundogan would be some midfield (Doubt Barca would let him go at any price though)
Rakatic 28 ... great player but I'd doubt if it's him.
Messi 28 ... I think he could struggle in England but wouldn't we love to try it. Maybe the time is right?