GroundBound
You have to decide how much you can afford to spend (there is no obvious point at which you get especially good value; the more you pay the better a plane you can get) and what sort of flying you want to do now and in the future.
If you want to fly VFR only then you can probably get something good enough for say E60k. If you want to fly IFR then you are looking at a lot more.
Unless you do more than about 200 hours a year, it will be cheaper to rent by the hour. But if that was the whole story then almost everybody would take a train and not own a car. By owning you can look after it well, make sure everything works, and have total access to it. It is impossible to put a price on these things.
Owning will also enable you to do many more hours because the marginal cost per extra hour flown is very low, much less than renting the cheapest crappiest plane you can find. So you will get more currency. Very few pilots who rent have enough currency because the hourly cost is so high.
But beware when buying - always get a full inspection - cost likely E1k or so. Many people sell their planes when they discover something they don't want you to know! "Suprise" annuals costing E10k are fairly common on 30 year old planes.