The first few times, I usually rent, or make do with something similar that I already have (depending on the activity, sometimes you can do this). Then, if I think that (a) I’m going to enjoy this activity, (b) I have a chance to do this with some regularity, and ( c) I can get reasonably good at it, I will buy. The advantage to having your own equipment is that you get it customized to your body size and to your level of expertise. There is something of a vicious cycle in this. The better your equipment fits and suits you, the more you’ll enjoy the activity, and the faster you’ll get better at it. Then when your level of expertise increases, you’ll be ready for yet another round of equipment buying.
As for buying what you need or what you hope to grow into, I would aim for something just a bit beyond your current level of expertise. That will get you to that level sooner.
Take skiing, for example. If you’re a solid intermediate skier, you should buy beginning advanced skis (that is, skis for advanced but not expert level).