Congratulations on your first art studio :) When I draw anime I use Charcoal pencils. If you want to outline the picture the heavier pencils are great and they are also great for shading. I usually out line my anime pictures my self but I always use a little shading here and there.

I am unsure of the desk part, sorry about that.

For GREAT drawing supplies for an anime style, outside of computer anyway are really simple but can be expensive.

Most medium used these days are Copic Markers. They do run expensive at about $3.50 - $5 per marker depending on where you buy them but they are really professional and go on very smoothly. You can also buy air spray to use to make the markers go down even smoother and softer, and also the markers have refill inks.

You also will need some good multiliner pens. Copics makes good ones and I also really enjoy Pilot multiliner pens too,

A lightbox will always be good for drawings, especially if your sketches are very messy and hard to erase. Put down the original sketch and lay a paper over it, and once you flick on the light box you can see through it and go towards inking.

Aside from that lots of junk paper for sketches and nice marker paper to use for final products.

For cheaper solutions you can use prismacolor pencils or markers but I really ssuggest the copics if you can get your hands on them.

Good luck!