When it comes to crochet thread and making Irish Crochet lace, it is best to invest in the best quality of thread. There are several companies that produce very good thread.
For Traditional Irish Crochet I like to use DMC Cordonet Special. This thread comes in 8 different sizes. What size of thread to use and what hook size to use with what size is explained in the Irish Crochet Lab website. Follow this link to read more >>>> DMC Thread
Next to this thread I also recommend thread from Presensia Fincrochet. To read more follow the link >>>> Fincrochet Thread
In Traditional Irish crochet the finest thread and finest crochet hooks were used to create the most delicate lace. To achieve the best results it is important to practice first with thicker thread and learn to crochet tight. All your stitches have to be uniform and neat. if you never before crocheted with fine thread and hooks, it can be a challenge at first, so use thread #10 for PC (packing cord), #20 - 30 for working thread (for motifs), and #60 for background netting. Crochet small projects at first.
Later, when you will become more comfortable with crochet even and neat stitches, start using finer thread and finer hooks:
#10 - for PC; ##60 - 80 for working thread, and #100 for background netting.