Welcome to TFP! Good to have you here
When I first started out, I gained a lot from this thread:
TFPC for Beginners
You'll read about testing, and for Trouble Free Pool Care (TFPC), you'll need a drop-based test kit such as a TF-100 or Taylor K-2006. It's the only option because test strips and pool store testing provide too many incorrect results for reliable pool care.
Your filter won't be able to kill or capture live algae. Only a sanitizer in the water can do that, and chlorine is the most effective sanitizer. The filter will gradually remove the dead algae "carcasses" after they're killed with chlorine. We use a process called a SLAM to completely kill the algae, and then after that it becomes pretty easy to keep the chemistry in range, and your water will be safe and sparkly.
You won't need any algaecides or other expensive chemicals from the pool store, so you'll save back the cost of a test kit very quickly.