Your first spell can have you nervous that you’re gonna mess up, get something wrong, or just have nothing happen. But that’s okay! It’s your first spell for a reason, and it will be a learning experience whether it’s successful or not.
My answers are no and no. This is all going to depend on your particular tradition or style of magic. It’s been years since I’ve cast a circle, but I create sacred space in my own way. I don’t cleanse the entire room before I work magic either. I find that it isn’t usually necessary and just adds an extra step to what I’m doing.
That being said – doing both of these things isn’t a bad idea, either. It just depends! If you feel like you want to cleanse the space and cast a circle for your first spell, go right ahead.
In my opinion, a good first spell to cast is going to be one you need but also one that doesn’t have too many steps or ingredients involved. That will help keep you from getting overwhelmed by the steps or forgetting ingredients. It’s helpful for it to be one you need, too, so you already have an emotional connection to what you’re doing. If you can’t think of a spell to cast, then I’d say protection spells and self-love spells are always great options!
Pardon me for asking, but if you aren’t sure how to reach out to her, how do you know she’s chosen you?
Supplies like we think aren’t necessary, especially when you’re first starting out. An offering bowl can be a bowl from your kitchen. A chalice can be a cup. An offering plate can be a plate from your kitchen. I mean, the options are endless when you look at what the object is at its foundation rather than what it is on the surface.
One way to reach out to deities is through prayer. If you’re planning on working with or worshipping Diana, I would start with researching her mythology and customs. Learn some traditional prayers for her, but also pray from the heart. It may also be helpful to learn a divination method or keep a dream journal so you can also receive messages from her, too.
I hope this helps! I’d also recommend checking out these links, too.
→ Confidence in Spellcasting
→ My Spellwriting Process 
→ Deity Altars: Prayer and Offerings at Home
→ Diana’s Love Devotional Prayer
→ Diana of the Moon Incense