It sounds like you're learning contemporary wushu kung-fu.
In contemporary and traditional wushu, most teachers will start you off with empty-hand training before moving on to weapons.
Just so we're clear on the terminology, "empty hand" refers to bare handed, without any weapons.
What puzzles me is that you said your teacher gave you a choice between "taiji" and "empty hand". You chose empty hand, but your teacher started you with weapons.
First of all, Taiji is done both with and without weapons. It tends to start you out without weapons and then adds the pole, straight sword, and other weapons later.
So what really happened was that your instructor was giving you a choice between Taiji and Wushu. You chose Wushu.
Both contemporary and traditional wushu are typically taught by first learning the basic stances, then learning basic punching, kicking, and blocking techniques. Then you move on to drills that have you moving while doing those and conditioning your body. Then you move on to memorizing empty handed forms (no weapons).
After that, wushu typically adds weapons. Contemporary wushu adds them fairly quickly compared with traditional wushu. The time varies by instructor, but it's very common to start training in weapons after 2-3 years of doing traditional wushu and after the first 3-6 months of doing contemporary wushu.
The reason why empty hand stuff is trained first in wushu is that it's much easier to learn the basics that way. Then when weapons training is added, that helps you with your strength, balance, and full body coordination. It can magnify problems particularly in your frame and balance that empty handed training didn't reveal.
Some people also find weapons training more intuitive. For example, if you're swinging a sword, you can see the sword and have a goal for that particular movement (for example, to thrust the tip straight forward or to drag the blade edge across horizontally). It's easier to see when you make a mistake. But in empty handed training, the goal of the technique is sometimes not easily understood. So it can be harder to know when you've made a mistake with empty handed training.
What's the right way to learn? Meh. It doesn't matter. Eventually if you keep going and learning stuff, you'll be fine.
You might want to ask your instructor, though, why she started you with weapons instead of empty-hand. It's possible it was a miscommunication to begin with. She might have thought you wanted to avoid empty-hand training and stick with weapons, instead. Ask her.
Hope that helps.