Hi Ian, welcome to the forum
My step-dad is also a DJ, and he uses CDRs made by Taiyo Yuden (order online or just look for “Made in Japan” on packaging in regular stores).
For software, we either use Burrrn (for converting music files to regular .cda) or CloneCD. But as Geno says, most burning software should do the job.
You can also burn with Itunes (as my step-dad does with the music he buys online) - just make sure, whatever software you use, to set the burn speed to 16x (gives best results with audio IMO).
I don’t know much about lappy burners, so can’t be of much help there I’m afraid. Hopefully another member can advise on that one.