A K6-III or K6-2+/3+ would definitely increase performance, as any of those CPUs have on-die L2 cache. In fact, the performance boost is quite appreciable, because most of the time this cache enables the avoidance of cacheable limits on motherboard chipsets.
That being said, I notice that the link you've provided is actually a K6-2+. That could certainly work, but the issue with the K6-2+ and K6-3+ is that they require 2.0 volts. You can run them at 2.1, and maybe 2.2 volts. At 2.2 volts, you're running some risks, but it can be done with proper cooling and a good CPU sample.
If you can run a CPU with 2.0 volts on your motherboard, the only appreciable differences between a K6-2+ and K6-3+, as well as a K6-III are as follows:
- The K6-2+ has 128kb of L2 cache, but otherwise shares the same core as the K6-3+
- Like the K6-III, the K6-3+ has 256kb of L2 cache
- K6-IIIs run at 2.2v, and don't overclock too well
- K6-2+s and K6-3+s overclock fantastically, and can even be overclocked/underclocked by software
The only other thing to make sure is that, if you go with the "+" CPU, your BIOS is compatible. Usually that's not too big of an issue, but it can be if you're using an OEM motherboard.
Anyway, I hope that this helps!