A silpat, or parchment paper. Gluten free doughs and batters are sticker than their standard counterparts. Prevent sticking wherever possible.
A stand mixer. No, this isn't an absolute necessity. But for a few things, it comes close. Since gluten free doughs and batters do not (by definition) contain gluten, it's nearly impossible to overbeat them. However, a lot of them - especially bread doughs - require a long beating period to incorporated enough air to be successful. As some batters are also heavy, a hand mixer may not be up to the challenge. And your arm certainly isn't.
Various baking pans. Arm yourself with the standard arsenal: An 8- or 9" square, a set of 8- or 9" rounds, a 9"x13", a bundt pan, a tube pan, loaf pans, cookie sheets, a springform pan, and a "jelly roll" 1/2 sheet pan. It's my tactic to usually acquire pans as I need them. Especially specific shaped pans that I might not use often. A pie pan (or three) is also a basic requirement. I prefer glass for filled pies, and metal for blind baking.
Piping bags and tips - One or two vinyl piping bags and a couple basic tips should get you in position to manage macarons, eclairs ,and other pastries. Plus, they make frosting cupcakes and filling cookies super easy.
Dishers in various sizes - these ice cream scoop-like tools range from melon-ball to 1/2 cup capacity or more. I use them in multiple sizes. You cannot believe how sticky some gluten free cookies and cake batters can be. This will make portioning them SO much easier.
Mixing bowls in multiple sizes. Especially one really big bowl for mixing flours. This will allow you to make up a batch of flour to store, making baking-on-the-fly a lot easier. Which leads us to:
Cannisters for flour storage. I like the Oxo ones with the push-button lids. It's not a bad idea to store gluten free flours and mixtures in the fridge or freezer to prevent them from spoiling.
Measuring spoons and cups. Two sets are a big help. Because of the various adjuncts, gluten free recipes can be more complex. And accurate measurement is essential.
Silicone spatulas and a bowl scraper. See above reference to the general stickiness.
An instant-read probe thermometer. Gluten free baked goods don't always brown or respond in the same way that their wheat-based counterparts do. Sometimes you might want to check the internal temperature (especially with breads). They're also handy for candy-making, in lieu of an actual candy thermometer.
And that should be enough to get us ready to go...