If that old PM3207 scope works then do get that. That's a decent scope for a beginner and the price is a steal. Probes can be obtained online cheaply, for a 15MHz scope you don't need anything expensive.
The cheap DIY kit "scopes" are toys that are very much completely useless - very low bandwidth (often in tens of kHz tops), low sampling rate, lack proper probes, horrendous user interface, etc. I have tested one, it wasn't able to show even a 20kHz sine wave properly - i.e. useless even for audio. Those gadgets are just a microcontroller with an LCD using the internal ADC for digitizing the signal + power regulator and a few buttons. Don't waste your time and money on that.
Later on start saving and you can get a very good modern digital scope for some 300-400 euro already - that is more useful for digital stuff because you get single shot captures, you get various serial protocol decoders, etc.