The answer to your question is "it depends". It depends on what kind of potato you're planting, or whether you want baby potatoes with tender skins that should be eaten sooner rather than later or large potatoes with thicker skins. To help you think about it you might find the following information useful.

Potatoes usually take about 90 – 135 days to mature before you harvest them. That means if you plant potatoes about July 15^th, they should be ready to harvest about mid-October to mid to late November. Potatoes don’t respond well to frost and your average first frost is about October 20^th according to the Farmer’s Almanac so you’ll want to harvest them before the first frost.

You can check with the place where you buy your seed potatoes about how long they take to mature. If you enjoy new potatoes, they’re usually ready in 6 – 8 weeks which is also a possibility.

For more information about growing potatoes you can read Potatoes (osu.edu) which tells you about planting potatoes, diseases, and pests and how to deal with each challenge. Also,  Growing Potatoes in a Home Garden | University of Maryland Extension (umd.edu) may prove helpful.