A scale. These recipes are provided by weight and not volume measurements which are imprecise. Ultimately you will be going by feel but starting with the correct measurements is helpful.
A surface. You should have a flat and stable surface (a counter or table) that is easy to clean and large enough for you to maneuver on. Wood is the best for pasta but not necessary.
Basic pots and pans including a large pot to boil water and fry and sauce pans for sauces or condimenti.
A wooden spoon and a spider/hand held strainer/slotted spoon for fishing pasta out of the pot (draining in a colander can damage delicate homemade pasta).
A pasta machine, useful if you are planning to work with egg based dough frequently and very useful for stuffed shapes.
Rolling pin, wooden dowel, or mattarello for rolling out dough (some shapes and doughs are better with a rolling pin and don’t take well to a pasta machine). A wine bottle will work in a pinch.
A knife and a few tools for cutting. A pizza cutter or a knife is totally serviceable but investing in a few specialized cutting tools can make things easier.
For specialized equipment check out sources like Aguzzeria del Cavallo in Bologna, etsy, webstaurant store, your local Italian specialty foods shop, or more conventional cooking equipment retailers like Williams Sonoma, Sur la Table, Target, etc. You can really go wild here with super ornate boards, extruders, molds, or even a chitarra.