Make sure you leave sufficient budget for the other items you will need. Bench power supply. Multimeters. Soldering iron. Scope probes. 4mm banana flying lead. Signal generator. Hook up wire and copperclad (unetched) PCB, or stripboard. A basic component kit. Diagonal cutters and pliers.
If you are considering second-hand equipment, then you can get scopes much much cheaper than $300; just make sure it is working.
All equipment has a learning curve, which means a beginner is often better served by having simple easily understood equipment. Beginners should be learning fundamental electronics, not spending too much time on the GUI of one manufacturers 2024 entry level equipment.
A good engineer will always be looking for simple easy ways to do the job. Once upon a time recording a scope trace required Polaroid cameras or pen plotters. Now the simplest and fastest way to record the complete experimental setup and all measurements is with a phone or digital camera (ah, bliss. The past wasn't always golden