I recently bought a Druine Turbulent, which has been an absolute hassle and tied up all my finances for over a year sorting it out. This is exactly what you don't want to happen at your stage. But now it's flying I rather like it and I wish I'd bought something similar , (albeit without all the faults) ages ago. I could have certainly been more savvy in buying the aircraft, but I did pay for a pre-buy inspection, so... be wary.
It illustrates the difficulty in owning something. If there's an issue, you are grounded until you can sort it out. But if you buy into a non-equity group and something goes tech you can just walk away and it's someone else's problem. There's a lot to be said for that.
On the other hand there is a learning curve to aircraft ownership, and I'm still in the foothills... But this isn't a learning curve that you learn much about by renting. By the time I'd finished my PPL I had time on 3 types of SEP. By the time I soloed in the Turbulent I had time in 5 more types. But to be honest I was a better pilot when I had my newly minted license. I'd done 45 hours in the previous 2 months, whereas when renting I tended to do far fewer. I suppose it depends on your skill level, but I didn't feel more prepared through having waited before ownership.
Over the past calendar month I put in over 8 hours on the Turbulent (partly in a frenetic rush to keep my licence!) for a marginal cost that is less than the cost of an hour in the 172 I used to rent. Because of cheapish hangarage where I live I'm optimistic that I can get a whole lot more flying in for the same disposable income, and do more interesting things with it - beforehand I couldn't afford to fly for more than an hour or two in any given month.
So... buying a small cheap aircraft (good single seaters can be very affordable) was a formula that could have worked for me at your stage... And arguably worked much better than flying around for short distances at great expense in typical hire aircraft (e.g. 152, 172). Your circumstances might be different, but if you can afford to buy an aircraft and keep a few hours in if it goes tech... Then I don't see why not.