Putty knives:

Choose metal over plastic. These are either stiff or flexible. You will find more use for the flexible ones. The stiffer knives are mostly for scraping and prepwork. Also come in many various widths, styles, with two side profiles - tapered or squared.
A square-sided one is preferred for wallpapering.

Borrow as many as you can, but get at least one good flexible squared 6", even if you have to buy one.

Break-in a brand-new one. Round-off one corner by scraping on your neighbour's concrete sidewalk - then make that dulled corner recognizable at a glance by marking   one corner and then the flip side with a felt pen. Keep this corner foremost when making cuts. The rounded corner won't snag your paper as you drag it.

Use a putty knife as a smoother in tight spots, as between a door casing and wall.

When double-cutting in those same tight spots, a flexible one is indispensable for holding the paper in place.

Serves as a straight-edge too, should you find need of one.
When making your cut, keep the guide (putty knife) between the wallpaper and your cutting knife. That way, a slip won't damage the paper, plus the cut will never be too shy.

Sponges:  (see: when inlaws pop in unannounced.)