Zone 6a Ohio.
Looked up NY - wow, there is a lot of zones there! Zones range from 3b to 7b in the state of NY! Looks like the zones 6a and 6b are fairly confined to finger lakes and great lakes area, or closer to LI. I attached a pic.
Seedlings. I don't usually separate seedlings, I just cut off the stems of the ones I'm not keeping. I've started seeds as early as January, but they were an alpine strawberry seed that was an approx 30 day germination! Usually you'll start seeds around late Feb/March. Plant usually around Mother's day or later.
But, there are exceptions. Direct seeding: put seed directly into the ground where it will grown for the season/ do not start in pots to transplant. Some seeds do best with direct seeding, such as squash, and melons and root vegetables like radish/carrot/beet/turnip. Melons won't germinate until soil is a certain temp, so don't direct seed too early bc seed could rot. Although squash and melons like to be direct seeded, you can start in pots, but they should be the kind you can plant in the ground as squash and melons don't like to be transplanted. A turnip and radish are fairly quick growing, so direct seed.
Early direct seeding. Some plants don't mind the cold, and you might be able to seed these late Feb/early March (barring an ice storm, for example): lettuce, peas, beets, turnips, radish, as examples.
Late plantings: some things do best when they get "kissed" by frost later in the season. Brussel sprouts and beets and carrots are good examples here...they get a bit sweeter when the plant gets a mild frost exposure. Or they do better when they can grow during hot weather, but mature and don't bolt when it is cooling off in Sept/Oct. Lettuces, spinach, others. FWIW, you can overwinter carrots in the ground to dig up when you want a fresh carrot in the fall/winter- just cover the row with a thick layer of straw and dig as desired.
Potatoes: These can be direct planted early spring. But, cut up a seed potato into 2-3 pieces, each with an eye. Some small seed potatoes don't need to be cut up, just plant with an eye facing up in the dirt. Let cut seed potatoes dry out for a day or two (helps prevent it from just molding in the ground - but not a required step), then plant. They will start when ready. Wait until plants flower then die back. Water well when they are flowering and until they just start to die back, then lay off the watering. Wait a couple weeks post die off, dig up your spuds. If you notice spuds trying to peek up at the soil line, cover them with dirt - otherwise they will turn green/not edible.
Have fun - lots to learn in the first couple of years of gardening.
