It's rare for a classmate to invite you to a birthday party. Even if you don't have a good relationship with her, you still have to give her face, not to mention that she is a girl. If you don't go, it will make the relationship worse.
When giving birthday gifts to classmates of this kind, you must be careful. Don't give them casually, otherwise you will make some jokes. If the relationship is not close, there is no need to give very expensive gifts, and don't give gifts that will cause criticism, unless you have a crush on her or like her. Haha, it's more appropriate to give her some crystal ornaments and some simple blessings on them. Blessing chocolates, plush toys, makeup mirrors, sun jars, etc. are recommended.
Of course, you can also give her some anime peripheral items she likes. It is also a good way to cater to her preferences. I hope it helps you.