By buying stocks, am I as an individual measurably affecting the economy?
From an aggregate level, the only direct income effect is that you will have paid a brokerage fee, which is part of the financial sector’s revenue.

After that, all that has happened is a rearrangement of an existing financial asset. If the seller uses the proceeds to purchase goods and services for consumption, that could be attributed to the purchase, although that might be a stretch.

The seller may also pay capital gains tax, and since they need a buyer to sell, that could be pinned on the purchase.

The effect on the price is hard to judge. In the short term, there might be some effect (although it would be negligible for a large cap firm), it will not really matter in the long run, if we assume that prices drift towards the fair value determined by corporate profitability.