Congrats on the new pond!

The aeration from a bottom diffuser is primarily to benefit your fish. Warm water has a significantly lower saturation level for dissolved oxygen. It is possible after several windless days in August that the oxygen levels get so low that your largest fish will start dying. Properly placed and sized diffusers will prevent that.

A pond of your depth will almost certainly stratify during warm weather, with the cooler bottom water becoming almost completely oxygen depleted. It is possible during the late spring, that a cold rain running into the pond will cause the pond to "turn over" and the oxygen-depleted water will get pushed into the upper layer. That can also cause a fish kill due to oxygen depletion. The diffusers also help avoid that rare, but painful, event for your pond.

An aeration system will not materially affect the plants or algae growth in your pond. If you have water, sunlight, and nutrients, then some photosynthesizing organisms WILL grow in your pond. As your pond matures, the nutrients will increase from their starting point and that is the reason the older ponds in your area generally have battles with weeds and algae.

You should probably read some of the threads in the archives about preventing filamentous algae, and some about beneficial plants.

Good luck on developing your pond. I predict a lot of fun in your future!