When is the right time to invest in your own pair of skates? And it is an investment - a decent pair of skates will start in the $100 range and that's not including the blades, which are generally purchased separately, and will start out at $100 also.
Some people find great joy in gliding around in a pair of rentals day in and day out. Others have specific goals in mind, such as spins, and when you begin to have goals that require a certain level of technical skill, consider purchasing your own pair of good skates. Good skates.
The hallmarks of a good-fitting pair of skates are a snug glove-like fit around the entire foot (especially at the heel), and good ankle support. After fully lacing up your skates, you should be able to wiggle your toes very slightly and you should definitely not feel as though your foot can move around in the boot easily. Consider these three factors when choosing your boot: your skating level, your weight and how often you skate. Work with a good skate fitter at your pro shop to get the best possible fit.
Finally, do not waste time and money investing in boots that are too stiff, hoping that they will last longer. You will quickly stop using them out of sheer frustration (because you can't bend your ankles and skate properly) and pain (because, well, just pain). Brand new skating boots hate to sit quietly in your closet. Boots should be stiff enough to take a few weeks to break in, depending on how often you skate. After all, you are softening up leather to conform to your foot's contours so there is a breaking in period, but they should never feel as though they're taking "forever" to break in.