If you're looking for the products he used, don't! It's all extremely expensive, apparently professional-grade stuff.
Why are you still reading? Go away!
Okay, you wore me down. Here they are:
Copic Marker SB12 12-Piece Sketch Basic Set $52.00. There are many, different other sets, but this is a representative selection. Other sets are greater sizes, specific color ranges (eg skin tones).
Copic Multiliner SP Waterproof Pigment Ink Pens Set B, Pack of 4, Black Ink (MLSP4B) $32.00. Again, other different selections exist with different nib selections.
Fair warning. 12 marker set of copic sketch at Michael's is $109. http://www.michaels.com/copic-sketch-marker-set-12-color-basic/D037662S.html
Same set on Amazon is Copic Marker 12-Piece Sketch Basic Set https://www.amazon.com/dp/B000MRR3GU/ref=cm_sw_r_cp_apa_XnUZzbJRR58NH
If you aren't getting 50% off at Michael's your are getting ripped off.
Try thinkgeek.com
What about copic markers? People use them to colour in anime/manga drawings and they are quite expensive so it's hard for people to buy them themselves. Most people that draw anime/manga would die for these.
Copic markers <- This is slightly over your budget but you might be able to find cheaper somewhere else.
I'm gonna chime in here and suggest you might skip the Black Ink kit. There's tons of different options for inking artwork in black in all sorts of price ranges and it's a technique that doesn't really capture what is unique about Copic style marker art. Don't get me wrong, you are probably going to want a black Copic, but less for inking outlines and more for filling in large black areas that you have already inked. My suggestion for what you should get? Honestly no matter what you get you are going to want more soon lol. $80 is going can get you a set of 12, this is as good a place to start as any: https://www.amazon.com/Copic-Marker-12-Piece-Sketch-Basic/dp/B000MRR3GU/ref=sr_1_2?ie=UTF8&qid=1479745724&sr=8-2&keywords=copic
That will give you a good sense of how the markers behave and blend, markers that are close in number blend well into one another.
On that note if you're coming up it's important to understand the numbering system that Copics use. It's simple and you can check it out here: https://imaginationinternationalinc.com/copic/101/copic-color-theory/
Last piece of advice is don't go too dark with your first set (colours ending in 8 or 9) as they are so dark they almost look black and it makes them tough to blend. I made this mistake thinking I wanted really intense tones but I hardly use those markers at all.
Have fun out there!
Oh! One more thing... I'm not sure where you live, but Michaels in Canada always has 40 or 50% off coupons online so that could help a lot if you have the same where you live.
Does anyone know anything about those pens?
EDIT: Actually found them after some googling. Has anyone used these? https://www.amazon.com/Copic-Marker-12-Piece-Sketch-Basic/dp/B000MRR3GU
Are you set on getting a 36 set of Copic Ciao's? If not I would actually recommend getting the:
Copic Marker 12-Piece Sketch Basic Set
Copic Markers 6-Piece Sketch Set, Skin Tones I
and some Copic Multliners (if you don't own some already)
If you are buying the makers from an actual store I also recommend picking up a few individual markers if you know you will need a specific color not included in the sets for your character.
If you are planning to buy online I personally recommend using dickblick.com and adding some individual colors to your cart as well.
Sketch markers seem to last a bit longer than the Ciaos and it is a bit easier to get replacements for Sketch markers since they actually have color numbers/names on their caps and they can be bought separately.
[EDIT] Make sure to get the proper paper as well if you plan to use these guys since they bleed like crazy if you use thinner paper. I used to use cardstock since it was pretty cheap and easy to buy in bulk from stores nearby.