My mother once told me how I started my career in the electrical arts, around the age of two or three years old, by sticking her surgical scissors (she was a Registered Nurse) into an electrical outlet while we were living in Denver, CO. I don't actually remember that experience, but apparently it had a significant effect on my later choice of a career path. Well, that and other survivable experiences along the path to adulthood.
I do like the μA741 and its "look-alike" dual op-amp counterpart, the MC1458. Both are unconditionally stable with just about any gain or load impedance without requiring external frequency compensation components. This series of ancient op-amps followed on the huge success of the μA709 integrated circuit op-amp, which does require external RC frequency compensation for stable performance at low closed-loop gains. So even if you can find some 709 op-amps at really cheap prices, avoid them. They are likely to be counterfeits anyway.
I would recommend using dual ±15 V power rails to practice learning how to actually use op-amps. There is more to using them than just as amplifiers and waveform clippers. Integrators, differentiators, oscillators and summing amplifiers are just some of the common uses for op-amps. Using a relatively higher voltage (±15 V) bi-polar power supply makes it easier to measure and understand these circuits.
Of course those early op-amps leave a lot to be desired in comparison with modern op-amps. Their input impedance is lower, their common-mode rejection ratio is lower, their input bias currents are higher, their input offset voltages are higher, their bandwidths are less, and their output drive capability in terms of voltage swing, as well as current capability, is less than most modern integrated circuit designs. Just about any parameter you can think of related to op-amp performance is hugely improved with less cost using modern designs. Today we have FET-input op-amps with almost infinite input impedance and practically zero input bias current; rail-to-rail op-amps whose outputs can swing very close to the supply voltages applied; short-circuit proof op-amps that don't self-destruct at the blink of an eye when their output is shorted to ground or to a power supply rail; and hybrid power op-amps that can deliver amperes of current to a load.
The operational amplifier options available today are almost limitless, but I would begin the learning process with either the 741 single op-amp or the 1458 dual op-amp. Letting the "magic smoke" out of a few of either of these will not bankrupt you. Just remember to bend the "legs" under each device you ruin, so as to not mistakenly try to use it again. Then throw the "dead bugs" in the trash when you clean up your workbench.