For the love of [preferred deity], keep that thing!
For sure it won't fulfill every oscilloscope need you may ever have down the road, but if it works reliably, then it is a great starter scope. Among other things, then it is kinda hard to accidentally burn the inputs out if you are unlucky with some connections, perfect for a beginner.
More to the point: If you, as a beginner, is doing something that scope can't cope with, then you are probably in
way over your head.
Also, once you do hit its limitations, then you will be in a much better position to judge what its successor should be capable of. In all likelihood you will decide to keep the old scope, as there are problems they still excel at, even when faced down by modern, kilobucks digital oscilloscopes.