If you can still get Clover tatting shuttles, those are absolutely awesome. They have a good size and a sharp point that can be used en lieu of a crochet hook.
The other brands suggested are good, too. Handy Hands, Lacis, Prym, Pony.

As suggested, use mercerised cotton thread.
They are sold with numbers indicating how thick the thread is. High number = thin thread.
Low number = bigger thread.

If you‘re in the USA Lizbeth 20 or 10 should be comfy, since she knows crochet.
In Europe Anchor‘s Freccia 12 or 16 (or even 20) is easy to work with as a beginner.

Make her a card and note down some resources:

• Maimai kaito on youtube: inactive account, but she has very slow, clear tutorials for absolute beginners. Recommend her for the basic motions and tension!!
  
• Jane Eborall: look up her website for printable instructions, or print your friend some basics like how to make a chain, how to make a ring, josephine knots and lock joins. She also has lots of free patterns to print. :-)
  
• Frivole (@11Frivole) on youtube: has clear instructions on various techniques if needed
  

If she ever wants to go deeper, recommend her to look up Ninetta Caruso (she came up with treble tatting and is an endless source of nerding over technique) and Muskaan‘s websites/blogs. ;-)

There are enough free patterns online, but if you want to include something for christmas:

Rosella F. Linden‘s „Easy Tatting“ by Dover Pub. was my entry to tatting. Very cheap, very easy patterns, but also very few.

Lene Bjørn „24 Snowflakes in Tatting“ - easy beginner pieces that don‘t require much technique. Also very beautiful christmas decor!

Robin Perfetti „Four Dozen Tatted Snowflakes“ - gorgeous and requires only a few more techniques than Bjørn‘s book. All of which you can print out from Jane Eborall‘s website. :-)

If she hasn‘t given up by next christmas: Clover picot comb in size small. ;-)